[
  {
    "problem_id": "HumanEval/109",
    "induction_tasks": {
      "count": 3,
      "tasks": [
        {
          "task_id": "induction_0",
          "task_type": "induction",
          "triple_id": "HumanEval/109_triple_2",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\n[4, 3, 1, 2]\n```\n```output_0\nFalse\n```\n\n\n# Message:\nDetermine if it is possible to get an array sorted in non-decreasing order by performing right shift operations on the given array. Parameters: arr (list): A list of unique integers. Returns: bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operations on the given array.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[4, 3, 1, 2]",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operations on the given array.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)"
          }
        },
        {
          "task_id": "induction_1",
          "task_type": "induction",
          "triple_id": "HumanEval/109_triple_8",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\n[2, 1]\n```\n```output_0\nTrue\n```\n\n\n# Message:\nDetermine if it is possible to get an array sorted in non-decreasing order by performing right shift operations on the given array. Parameters: arr (list): A list of unique integers. Returns: bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operations on the given array.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[2, 1]",
                "True"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operations on the given array.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)"
          }
        },
        {
          "task_id": "induction_2",
          "task_type": "induction",
          "triple_id": "HumanEval/109_triple_4",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\n[]\n```\n```output_0\nTrue\n```\n\n\n# Message:\nDetermine if it is possible to get an array sorted in non-decreasing order by performing right shift operations on the given array. Parameters: arr (list): A list of unique integers. Returns: bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operations on the given array.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[]",
                "True"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operations on the given array.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)"
          }
        }
      ]
    },
    "deduction_tasks": {
      "count": 2,
      "tasks": [
        {
          "task_id": "deduction_0",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_triple_1",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operations on the given array.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)\n\n# Input:\n[3, 5, 10, 1, 2]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operations on the given array.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)",
            "test_input": "[3, 5, 10, 1, 2]"
          }
        },
        {
          "task_id": "deduction_1",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_triple_3",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operations on the given array.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)\n\n# Input:\n[3, 5, 4, 1, 2]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operations on the given array.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)",
            "test_input": "[3, 5, 4, 1, 2]"
          }
        }
      ]
    },
    "abduction_tasks": {
      "count": 2,
      "tasks": [
        {
          "task_id": "abduction_0",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_triple_2",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operations on the given array.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "[4, 3, 1, 2]",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operations on the given array.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)",
            "expected_output": "False"
          }
        },
        {
          "task_id": "abduction_1",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operations on the given array.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "[3, 4, 5, 1, 2]",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operations on the given array.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)",
            "expected_output": "False"
          }
        }
      ]
    },
    "total_tasks": 7,
    "timestamp": "2025-07-23T06:32:45.709633"
  },
  {
    "problem_id": "HumanEval/109",
    "induction_tasks": {
      "count": 3,
      "tasks": [
        {
          "task_id": "induction_0",
          "task_type": "induction",
          "triple_id": "HumanEval/109_triple_6",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\n[5, 6, 7, 8, 1, 2, 3, 4]\n```\n```output_0\nTrue\n```\n\n\n# Message:\nDetermine if it is possible to get an array sorted in non-decreasing order by performing right shift operation any number of times. Parameters: arr (list): A list of unique integers. Returns: bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operation any number of times.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n    else:\n        # If no such element is found, the array is already sorted\n        return True\n\n    # Perform right shift operation\n    arr = arr[i + 1:] + arr[:i + 1]\n\n    # Check if the array is sorted\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return False\n\n    return True\n",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[5, 6, 7, 8, 1, 2, 3, 4]",
                "True"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operation any number of times.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n    else:\n        # If no such element is found, the array is already sorted\n        return True\n\n    # Perform right shift operation\n    arr = arr[i + 1:] + arr[:i + 1]\n\n    # Check if the array is sorted\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return False\n\n    return True\n"
          }
        },
        {
          "task_id": "induction_1",
          "task_type": "induction",
          "triple_id": "HumanEval/109_triple_4",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\n[]\n```\n```output_0\nTrue\n```\n\n\n# Message:\nDetermine if it is possible to get an array sorted in non-decreasing order by performing right shift operation any number of times. Parameters: arr (list): A list of unique integers. Returns: bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operation any number of times.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n    else:\n        # If no such element is found, the array is already sorted\n        return True\n\n    # Perform right shift operation\n    arr = arr[i + 1:] + arr[:i + 1]\n\n    # Check if the array is sorted\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return False\n\n    return True\n",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[]",
                "True"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operation any number of times.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n    else:\n        # If no such element is found, the array is already sorted\n        return True\n\n    # Perform right shift operation\n    arr = arr[i + 1:] + arr[:i + 1]\n\n    # Check if the array is sorted\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return False\n\n    return True\n"
          }
        },
        {
          "task_id": "induction_2",
          "task_type": "induction",
          "triple_id": "HumanEval/109_triple_5",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\n[1]\n```\n```output_0\nTrue\n```\n\n\n# Message:\nDetermine if it is possible to get an array sorted in non-decreasing order by performing right shift operation any number of times. Parameters: arr (list): A list of unique integers. Returns: bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operation any number of times.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n    else:\n        # If no such element is found, the array is already sorted\n        return True\n\n    # Perform right shift operation\n    arr = arr[i + 1:] + arr[:i + 1]\n\n    # Check if the array is sorted\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return False\n\n    return True\n",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[1]",
                "True"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operation any number of times.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n    else:\n        # If no such element is found, the array is already sorted\n        return True\n\n    # Perform right shift operation\n    arr = arr[i + 1:] + arr[:i + 1]\n\n    # Check if the array is sorted\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return False\n\n    return True\n"
          }
        }
      ]
    },
    "deduction_tasks": {
      "count": 2,
      "tasks": [
        {
          "task_id": "deduction_0",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_triple_4",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operation any number of times.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n    else:\n        # If no such element is found, the array is already sorted\n        return True\n\n    # Perform right shift operation\n    arr = arr[i + 1:] + arr[:i + 1]\n\n    # Check if the array is sorted\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return False\n\n    return True\n\n\n# Input:\n[]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "True",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operation any number of times.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n    else:\n        # If no such element is found, the array is already sorted\n        return True\n\n    # Perform right shift operation\n    arr = arr[i + 1:] + arr[:i + 1]\n\n    # Check if the array is sorted\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return False\n\n    return True\n",
            "test_input": "[]"
          }
        },
        {
          "task_id": "deduction_1",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_triple_7",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operation any number of times.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n    else:\n        # If no such element is found, the array is already sorted\n        return True\n\n    # Perform right shift operation\n    arr = arr[i + 1:] + arr[:i + 1]\n\n    # Check if the array is sorted\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return False\n\n    return True\n\n\n# Input:\n[1, 2, 3, 4, 5, 6, 7, 8]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "True",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operation any number of times.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n    else:\n        # If no such element is found, the array is already sorted\n        return True\n\n    # Perform right shift operation\n    arr = arr[i + 1:] + arr[:i + 1]\n\n    # Check if the array is sorted\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return False\n\n    return True\n",
            "test_input": "[1, 2, 3, 4, 5, 6, 7, 8]"
          }
        }
      ]
    },
    "abduction_tasks": {
      "count": 2,
      "tasks": [
        {
          "task_id": "abduction_0",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_triple_9",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operation any number of times.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n    else:\n        # If no such element is found, the array is already sorted\n        return True\n\n    # Perform right shift operation\n    arr = arr[i + 1:] + arr[:i + 1]\n\n    # Check if the array is sorted\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return False\n\n    return True\n\n\n# Observed Output:\nTrue\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "[2, 1]",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operation any number of times.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n    else:\n        # If no such element is found, the array is already sorted\n        return True\n\n    # Perform right shift operation\n    arr = arr[i + 1:] + arr[:i + 1]\n\n    # Check if the array is sorted\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return False\n\n    return True\n",
            "expected_output": "True"
          }
        },
        {
          "task_id": "abduction_1",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_triple_1",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operation any number of times.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n    else:\n        # If no such element is found, the array is already sorted\n        return True\n\n    # Perform right shift operation\n    arr = arr[i + 1:] + arr[:i + 1]\n\n    # Check if the array is sorted\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return False\n\n    return True\n\n\n# Observed Output:\nTrue\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "[3, 5, 10, 1, 2]",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing \n    right shift operation any number of times.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n    else:\n        # If no such element is found, the array is already sorted\n        return True\n\n    # Perform right shift operation\n    arr = arr[i + 1:] + arr[:i + 1]\n\n    # Check if the array is sorted\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return False\n\n    return True\n",
            "expected_output": "True"
          }
        }
      ]
    },
    "total_tasks": 7,
    "timestamp": "2025-07-23T11:56:43.285339"
  },
  {
    "problem_id": "HumanEval/109",
    "induction_tasks": {
      "count": 2,
      "tasks": [
        {
          "task_id": "induction_0",
          "task_type": "induction",
          "triple_id": "HumanEval/109_synthetic_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\n0\n```\n```output_0\nTrue\n```\n\n\n# Message:\nDetermine if it is possible to get an array sorted in non-decreasing order by performing right shift operations on the given array. Parameters: arr (list): A list of unique integers. Returns: bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing\n    right shift operations on the given array.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations,\n          False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "0",
                "True"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing\n    right shift operations on the given array.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations,\n          False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)"
          }
        },
        {
          "task_id": "induction_1",
          "task_type": "induction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\n[3, 4, 5, 1, 2]\n```\n```output_0\nFalse\n```\n\n\n# Message:\nDetermine if it is possible to get an array sorted in non-decreasing order by performing right shift operations on the given array. Parameters: arr (list): A list of unique integers. Returns: bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing\n    right shift operations on the given array.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations,\n          False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[3, 4, 5, 1, 2]",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing\n    right shift operations on the given array.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations,\n          False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)"
          }
        }
      ]
    },
    "deduction_tasks": {
      "count": 1,
      "tasks": [
        {
          "task_id": "deduction_0",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing\n    right shift operations on the given array.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations,\n          False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)\n\n# Input:\n[3, 4, 5, 1, 2]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing\n    right shift operations on the given array.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations,\n          False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)",
            "test_input": "[3, 4, 5, 1, 2]"
          }
        }
      ]
    },
    "abduction_tasks": {
      "count": 1,
      "tasks": [
        {
          "task_id": "abduction_0",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_synthetic_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing\n    right shift operations on the given array.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations,\n          False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)\n\n# Observed Output:\nTrue\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "0",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing\n    right shift operations on the given array.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations,\n          False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)",
            "expected_output": "True"
          }
        }
      ]
    },
    "total_tasks": 4,
    "timestamp": "2025-07-23T17:43:16.066817"
  },
  {
    "problem_id": "HumanEval/109",
    "induction_tasks": {
      "count": 1,
      "tasks": [
        {
          "task_id": "induction_0",
          "task_type": "induction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\n[3, 4, 5, 1, 2]\n```\n```output_0\nTrue\n```\n\n\n# Message:\nDetermine if it is possible to get an array sorted in non-decreasing order by performing right shift operations. Parameters: arr (list): A list of unique integers. Returns: bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing right shift operations.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(len(arr)):\n        arr = [arr[-1]] + arr[:-1]\n\n        # Check if the array is sorted\n        if arr == sorted(arr):\n            return True\n\n    return False",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[3, 4, 5, 1, 2]",
                "True"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing right shift operations.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(len(arr)):\n        arr = [arr[-1]] + arr[:-1]\n\n        # Check if the array is sorted\n        if arr == sorted(arr):\n            return True\n\n    return False"
          }
        }
      ]
    },
    "deduction_tasks": {
      "count": 1,
      "tasks": [
        {
          "task_id": "deduction_0",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing right shift operations.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(len(arr)):\n        arr = [arr[-1]] + arr[:-1]\n\n        # Check if the array is sorted\n        if arr == sorted(arr):\n            return True\n\n    return False\n\n# Input:\n[3, 4, 5, 1, 2]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_output": "True",
          "evaluation_data": {
            "program": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing right shift operations.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(len(arr)):\n        arr = [arr[-1]] + arr[:-1]\n\n        # Check if the array is sorted\n        if arr == sorted(arr):\n            return True\n\n    return False",
            "input": "[3, 4, 5, 1, 2]",
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing right shift operations.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(len(arr)):\n        arr = [arr[-1]] + arr[:-1]\n\n        # Check if the array is sorted\n        if arr == sorted(arr):\n            return True\n\n    return False"
          }
        }
      ]
    },
    "abduction_tasks": {
      "count": 1,
      "tasks": [
        {
          "task_id": "abduction_0",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing right shift operations.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(len(arr)):\n        arr = [arr[-1]] + arr[:-1]\n\n        # Check if the array is sorted\n        if arr == sorted(arr):\n            return True\n\n    return False\n\n# Observed Output:\nTrue\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_input": "[3, 4, 5, 1, 2]",
          "evaluation_data": {
            "program": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing right shift operations.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(len(arr)):\n        arr = [arr[-1]] + arr[:-1]\n\n        # Check if the array is sorted\n        if arr == sorted(arr):\n            return True\n\n    return False",
            "output": "True",
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing right shift operations.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain the sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(len(arr)):\n        arr = [arr[-1]] + arr[:-1]\n\n        # Check if the array is sorted\n        if arr == sorted(arr):\n            return True\n\n    return False"
          }
        }
      ]
    },
    "total_tasks": 3,
    "timestamp": "2025-07-23T18:23:15.462842"
  },
  {
    "problem_id": "HumanEval/109",
    "induction_tasks": {
      "count": 1,
      "tasks": [
        {
          "task_id": "induction_0",
          "task_type": "induction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\n[3, 4, 5, 1, 2]\n```\n```output_0\nFalse\n```\n\n\n# Message:\nDetermine if it is possible to get an array sorted in non-decreasing order by performing right shift operations. Parameters: arr (list): A list of unique integers. Returns: bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing right shift operations.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[3, 4, 5, 1, 2]",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing right shift operations.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)"
          }
        }
      ]
    },
    "deduction_tasks": {
      "count": 1,
      "tasks": [
        {
          "task_id": "deduction_0",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing right shift operations.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)\n\n# Input:\n[3, 4, 5, 1, 2]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "program": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing right shift operations.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)",
            "input": "[3, 4, 5, 1, 2]",
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing right shift operations.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)"
          }
        }
      ]
    },
    "abduction_tasks": {
      "count": 1,
      "tasks": [
        {
          "task_id": "abduction_0",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing right shift operations.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "[3, 4, 5, 1, 2]",
          "evaluation_data": {
            "program": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing right shift operations.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)",
            "output": "False",
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    Determine if it is possible to get an array sorted in non-decreasing order by performing right shift operations.\n\n    Parameters:\n    arr (list): A list of unique integers.\n\n    Returns:\n    bool: True if it is possible to obtain a sorted array by performing right shift operations, False otherwise.\n    \"\"\"\n    if not arr:\n        return True\n\n    # Find the index of the element that is out of order\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            break\n\n    # Perform right shift operations\n    for _ in range(i + 1):\n        arr.insert(0, arr.pop())\n\n    # Check if the array is sorted\n    return arr == sorted(arr)"
          }
        }
      ]
    },
    "total_tasks": 3,
    "timestamp": "2025-07-23T20:32:14.271223"
  },
  {
    "problem_id": "HumanEval/109",
    "induction_tasks": {
      "count": 1,
      "tasks": [
        {
          "task_id": "induction_0",
          "task_type": "induction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([3, 4, 5, 1, 2])\n```\n```output_0\nFalse\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n\n    return count <= 1",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "move_one_ball([3, 4, 5, 1, 2])",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n\n    return count <= 1"
          }
        }
      ]
    },
    "deduction_tasks": {
      "count": 1,
      "tasks": [
        {
          "task_id": "deduction_0",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n\n    return count <= 1\n\n# Input:\n[3, 4, 5, 1, 2]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n\n    return count <= 1",
            "test_input": "[3, 4, 5, 1, 2]",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n\n    return count <= 1"
          }
        }
      ]
    },
    "abduction_tasks": {
      "count": 1,
      "tasks": [
        {
          "task_id": "abduction_0",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n\n    return count <= 1\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "[3, 4, 5, 1, 2]",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n\n    return count <= 1",
            "expected_output": "False",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n\n    return count <= 1"
          }
        }
      ]
    },
    "total_tasks": 3,
    "timestamp": "2025-07-24T22:40:43.690865"
  },
  {
    "problem_id": "HumanEval/109",
    "induction_tasks": {
      "count": 1,
      "tasks": [
        {
          "task_id": "induction_0",
          "task_type": "induction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([3, 4, 5, 1, 2])\n```\n```output_0\nFalse\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if not arr:\n        return True\n    n = len(arr)\n    for i in range(n):\n        if arr[i] >= arr[(i-1)%n]:\n            continue\n        else:\n            return False\n    return True",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[3, 4, 5, 1, 2]",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n    n = len(arr)\n    for i in range(n):\n        if arr[i] >= arr[(i-1)%n]:\n            continue\n        else:\n            return False\n    return True"
          }
        }
      ]
    },
    "deduction_tasks": {
      "count": 1,
      "tasks": [
        {
          "task_id": "deduction_0",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True\n    n = len(arr)\n    for i in range(n):\n        if arr[i] >= arr[(i-1)%n]:\n            continue\n        else:\n            return False\n    return True\n\n# Input:\n[3, 4, 5, 1, 2]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True\n    n = len(arr)\n    for i in range(n):\n        if arr[i] >= arr[(i-1)%n]:\n            continue\n        else:\n            return False\n    return True",
            "test_input": "[3, 4, 5, 1, 2]",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n    n = len(arr)\n    for i in range(n):\n        if arr[i] >= arr[(i-1)%n]:\n            continue\n        else:\n            return False\n    return True"
          }
        }
      ]
    },
    "abduction_tasks": {
      "count": 1,
      "tasks": [
        {
          "task_id": "abduction_0",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True\n    n = len(arr)\n    for i in range(n):\n        if arr[i] >= arr[(i-1)%n]:\n            continue\n        else:\n            return False\n    return True\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([3, 4, 5, 1, 2])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True\n    n = len(arr)\n    for i in range(n):\n        if arr[i] >= arr[(i-1)%n]:\n            continue\n        else:\n            return False\n    return True",
            "expected_output": "False",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n    n = len(arr)\n    for i in range(n):\n        if arr[i] >= arr[(i-1)%n]:\n            continue\n        else:\n            return False\n    return True"
          }
        }
      ]
    },
    "total_tasks": 3,
    "timestamp": "2025-07-24T23:13:18.146342"
  },
  {
    "problem_id": "HumanEval/109",
    "induction_tasks": {
      "count": 6,
      "tasks": [
        {
          "task_id": "induction_0",
          "task_type": "induction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([3, 4, 5, 1, 2])\n```\n```output_0\nFalse\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[3, 4, 5, 1, 2]",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1"
          }
        },
        {
          "task_id": "induction_1",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([1, 2, 3, 4, 5])\n```\n```output_0\nTrue\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[1, 2, 3, 4, 5]",
                "True"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1"
          }
        },
        {
          "task_id": "induction_2",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([5, 4, 3, 2, 1])\n```\n```output_0\nFalse\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[5, 4, 3, 2, 1]",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1"
          }
        },
        {
          "task_id": "induction_3",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([1, 3, 2, 4, 5])\n```\n```output_0\nFalse\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[1, 3, 2, 4, 5]",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1"
          }
        },
        {
          "task_id": "induction_4",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([5, 1, 2, 3, 4])\n```\n```output_0\nFalse\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[5, 1, 2, 3, 4]",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1"
          }
        },
        {
          "task_id": "induction_5",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([])\n```\n```output_0\nTrue\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[]",
                "True"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1"
          }
        }
      ]
    },
    "deduction_tasks": {
      "count": 6,
      "tasks": [
        {
          "task_id": "deduction_0",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1\n\n# Input:\n[3, 4, 5, 1, 2]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1",
            "test_input": "[3, 4, 5, 1, 2]",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1"
          }
        },
        {
          "task_id": "deduction_1",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1\n\n# Input:\n[1, 2, 3, 4, 5]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "True",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1",
            "test_input": "[1, 2, 3, 4, 5]",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1"
          }
        },
        {
          "task_id": "deduction_2",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1\n\n# Input:\n[5, 4, 3, 2, 1]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1",
            "test_input": "[5, 4, 3, 2, 1]",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1"
          }
        },
        {
          "task_id": "deduction_3",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1\n\n# Input:\n[1, 3, 2, 4, 5]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1",
            "test_input": "[1, 3, 2, 4, 5]",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1"
          }
        },
        {
          "task_id": "deduction_4",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1\n\n# Input:\n[5, 1, 2, 3, 4]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1",
            "test_input": "[5, 1, 2, 3, 4]",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1"
          }
        },
        {
          "task_id": "deduction_5",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1\n\n# Input:\n[]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "True",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1",
            "test_input": "[]",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1"
          }
        }
      ]
    },
    "abduction_tasks": {
      "count": 6,
      "tasks": [
        {
          "task_id": "abduction_0",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([3, 4, 5, 1, 2])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1",
            "expected_output": "False",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1"
          }
        },
        {
          "task_id": "abduction_1",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1\n\n# Observed Output:\nTrue\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([1, 2, 3, 4, 5])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1",
            "expected_output": "True",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1"
          }
        },
        {
          "task_id": "abduction_2",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([5, 4, 3, 2, 1])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1",
            "expected_output": "False",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1"
          }
        },
        {
          "task_id": "abduction_3",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([1, 3, 2, 4, 5])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1",
            "expected_output": "False",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1"
          }
        },
        {
          "task_id": "abduction_4",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([5, 1, 2, 3, 4])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1",
            "expected_output": "False",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1"
          }
        },
        {
          "task_id": "abduction_5",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1\n\n# Observed Output:\nTrue\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1",
            "expected_output": "True",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True\n\n    n = len(arr)\n    count = 0\n    for i in range(n):\n        if arr[i] < arr[(i + 1) % n]:\n            count += 1\n        else:\n            break\n\n    return count == n - 1"
          }
        }
      ]
    },
    "total_tasks": 18,
    "timestamp": "2025-07-25T19:43:22.894571"
  },
  {
    "problem_id": "HumanEval/109",
    "induction_tasks": {
      "count": 24,
      "tasks": [
        {
          "task_id": "induction_0",
          "task_type": "induction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([3, 4, 5, 1, 2])\n```\n```output_0\nTrue\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[3, 4, 5, 1, 2]",
                "True"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False"
          }
        },
        {
          "task_id": "induction_1",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([1, 2, 3, 4, 5])\n```\n```output_0\nTrue\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[1, 2, 3, 4, 5]",
                "True"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False"
          }
        },
        {
          "task_id": "induction_2",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([5, 4, 3, 2, 1])\n```\n```output_0\nFalse\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[5, 4, 3, 2, 1]",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False"
          }
        },
        {
          "task_id": "induction_3",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([1, 3, 5, 2, 4])\n```\n```output_0\nFalse\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[1, 3, 5, 2, 4]",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False"
          }
        },
        {
          "task_id": "induction_4",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([1, 5, 3, 4, 2])\n```\n```output_0\nFalse\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[1, 5, 3, 4, 2]",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False"
          }
        },
        {
          "task_id": "induction_5",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([])\n```\n```output_0\nTrue\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[]",
                "True"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False"
          }
        },
        {
          "task_id": "induction_6",
          "task_type": "induction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([3, 4, 5, 1, 2])\n```\n```output_0\nFalse\n```\n\n\n# Message:\nWe have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The numbers in the array will be randomly ordered. Your task is to determine if it is possible to get an array sorted in non-decreasing order by performing the following operation on the given array: You are allowed to perform right shift operation any number of times. One right shift operation means shifting all elements of the array by one position in the right direction. The last element of the array will be moved to the starting position in the array i.e. 0th index. If it is possible to obtain the sorted array by performing the above operation then return True else return False. If the given array is empty then return True. For Example: move_one_ball([3, 4, 5, 1, 2])==>True Explanation: By performin 2 right shift operations, non-decreasing order can be achieved for the given array. move_one_ball([3, 5, 4, 1, 2])==>False Explanation:It is not possible to get non-decreasing order for the given array by performing any number of right shift operations.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[3, 4, 5, 1, 2]",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True"
          }
        },
        {
          "task_id": "induction_7",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([1, 2, 3, 4, 5])\n```\n```output_0\nFalse\n```\n\n\n# Message:\nWe have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The numbers in the array will be randomly ordered. Your task is to determine if it is possible to get an array sorted in non-decreasing order by performing the following operation on the given array: You are allowed to perform right shift operation any number of times. One right shift operation means shifting all elements of the array by one position in the right direction. The last element of the array will be moved to the starting position in the array i.e. 0th index. If it is possible to obtain the sorted array by performing the above operation then return True else return False. If the given array is empty then return True. For Example: move_one_ball([3, 4, 5, 1, 2])==>True Explanation: By performin 2 right shift operations, non-decreasing order can be achieved for the given array. move_one_ball([3, 5, 4, 1, 2])==>False Explanation:It is not possible to get non-decreasing order for the given array by performing any number of right shift operations.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[1, 2, 3, 4, 5]",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True"
          }
        },
        {
          "task_id": "induction_8",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([5, 4, 3, 2, 1])\n```\n```output_0\nFalse\n```\n\n\n# Message:\nWe have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The numbers in the array will be randomly ordered. Your task is to determine if it is possible to get an array sorted in non-decreasing order by performing the following operation on the given array: You are allowed to perform right shift operation any number of times. One right shift operation means shifting all elements of the array by one position in the right direction. The last element of the array will be moved to the starting position in the array i.e. 0th index. If it is possible to obtain the sorted array by performing the above operation then return True else return False. If the given array is empty then return True. For Example: move_one_ball([3, 4, 5, 1, 2])==>True Explanation: By performin 2 right shift operations, non-decreasing order can be achieved for the given array. move_one_ball([3, 5, 4, 1, 2])==>False Explanation:It is not possible to get non-decreasing order for the given array by performing any number of right shift operations.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[5, 4, 3, 2, 1]",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True"
          }
        },
        {
          "task_id": "induction_9",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([1, 3, 2, 4, 5])\n```\n```output_0\nFalse\n```\n\n\n# Message:\nWe have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The numbers in the array will be randomly ordered. Your task is to determine if it is possible to get an array sorted in non-decreasing order by performing the following operation on the given array: You are allowed to perform right shift operation any number of times. One right shift operation means shifting all elements of the array by one position in the right direction. The last element of the array will be moved to the starting position in the array i.e. 0th index. If it is possible to obtain the sorted array by performing the above operation then return True else return False. If the given array is empty then return True. For Example: move_one_ball([3, 4, 5, 1, 2])==>True Explanation: By performin 2 right shift operations, non-decreasing order can be achieved for the given array. move_one_ball([3, 5, 4, 1, 2])==>False Explanation:It is not possible to get non-decreasing order for the given array by performing any number of right shift operations.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[1, 3, 2, 4, 5]",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True"
          }
        },
        {
          "task_id": "induction_10",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([1, 5, 4, 3, 2])\n```\n```output_0\nFalse\n```\n\n\n# Message:\nWe have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The numbers in the array will be randomly ordered. Your task is to determine if it is possible to get an array sorted in non-decreasing order by performing the following operation on the given array: You are allowed to perform right shift operation any number of times. One right shift operation means shifting all elements of the array by one position in the right direction. The last element of the array will be moved to the starting position in the array i.e. 0th index. If it is possible to obtain the sorted array by performing the above operation then return True else return False. If the given array is empty then return True. For Example: move_one_ball([3, 4, 5, 1, 2])==>True Explanation: By performin 2 right shift operations, non-decreasing order can be achieved for the given array. move_one_ball([3, 5, 4, 1, 2])==>False Explanation:It is not possible to get non-decreasing order for the given array by performing any number of right shift operations.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[1, 5, 4, 3, 2]",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True"
          }
        },
        {
          "task_id": "induction_11",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([])\n```\n```output_0\nTrue\n```\n\n\n# Message:\nWe have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The numbers in the array will be randomly ordered. Your task is to determine if it is possible to get an array sorted in non-decreasing order by performing the following operation on the given array: You are allowed to perform right shift operation any number of times. One right shift operation means shifting all elements of the array by one position in the right direction. The last element of the array will be moved to the starting position in the array i.e. 0th index. If it is possible to obtain the sorted array by performing the above operation then return True else return False. If the given array is empty then return True. For Example: move_one_ball([3, 4, 5, 1, 2])==>True Explanation: By performin 2 right shift operations, non-decreasing order can be achieved for the given array. move_one_ball([3, 5, 4, 1, 2])==>False Explanation:It is not possible to get non-decreasing order for the given array by performing any number of right shift operations.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[]",
                "True"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True"
          }
        },
        {
          "task_id": "induction_12",
          "task_type": "induction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([3, 4, 5, 1, 2])\n```\n```output_0\nFalse\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[3, 4, 5, 1, 2]",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True"
          }
        },
        {
          "task_id": "induction_13",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([1, 2, 3, 4, 5])\n```\n```output_0\nTrue\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[1, 2, 3, 4, 5]",
                "True"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True"
          }
        },
        {
          "task_id": "induction_14",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([5, 4, 3, 2, 1])\n```\n```output_0\nFalse\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[5, 4, 3, 2, 1]",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True"
          }
        },
        {
          "task_id": "induction_15",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([1, 2, 4, 3, 5])\n```\n```output_0\nFalse\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[1, 2, 4, 3, 5]",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True"
          }
        },
        {
          "task_id": "induction_16",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([1, 2, 3, 5, 4])\n```\n```output_0\nFalse\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[1, 2, 3, 5, 4]",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True"
          }
        },
        {
          "task_id": "induction_17",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([1, 2, 3, 4, 1])\n```\n```output_0\nFalse\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[1, 2, 3, 4, 1]",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True"
          }
        },
        {
          "task_id": "induction_18",
          "task_type": "induction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([3, 4, 5, 1, 2])\n```\n```output_0\nTrue\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[3, 4, 5, 1, 2]",
                "True"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False"
          }
        },
        {
          "task_id": "induction_19",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([1, 2, 3, 4, 5])\n```\n```output_0\nFalse\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[1, 2, 3, 4, 5]",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False"
          }
        },
        {
          "task_id": "induction_20",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([5, 4, 3, 2, 1])\n```\n```output_0\nTrue\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[5, 4, 3, 2, 1]",
                "True"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False"
          }
        },
        {
          "task_id": "induction_21",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([1, 3, 2, 4, 5])\n```\n```output_0\nTrue\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[1, 3, 2, 4, 5]",
                "True"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False"
          }
        },
        {
          "task_id": "induction_22",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([1, 2, 3, 4, 1])\n```\n```output_0\nTrue\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[1, 2, 3, 4, 1]",
                "True"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False"
          }
        },
        {
          "task_id": "induction_23",
          "task_type": "induction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a set of input/output pairs and a message describing the hidden function. The Assistant must:\n\n1. **Privately think step-by-step** about how to reconstruct the general function based on the provided examples.  \n2. **Output exactly one** `<think>...</think>` block containing the full reasoning process.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the Python code snippet defining the function `f`—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.  \n5. Follow to the **code requirements** and **formatting rules**.\n\n# Code Requirements:\n- Name the entry function `f` (e.g., `def f(...): ...`), you may include nested definitions inside `f`.  \n- Ensure the function returns a value.  \n- Include at least one input parameter.  \n- Make the function deterministic.  \n- AVOID the FOLLOWING:\n  * Random functions or variables  \n  * Date/time operations  \n  * I/O operations (reading files, network requests)  \n  * Printing or logging  \n  * Any external state  \n- Ensure execution completes within 10 seconds on a modern CPU.  \n- All imports and custom class definitions must be at the very top of the code snippet.  \n- The snippet must end with a return statement from the main function `f`; anything after will be removed.\n\nUser:\n# Input and Output Pairs:\n```input_0\nmove_one_ball([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])\n```\n```output_0\nFalse\n```\n\n\n# Message:\nFind the function that produces these outputs from these inputs.\n\n# Assistant should follow this format:\n<think> \n# 1. Review each input/output pair and the message to understand the pattern.\n# 2. Infer the general algorithm or transformation being applied.\n# 3. Outline the structure of function `f` that would reproduce all examples. \n# 4. Ensure the function meets all requirements.\n</think> \n\n<answer> \ndef f(...): \n    # your code here \n    return ...\n</answer>\n\nAssistant:\n",
          "expected_solution": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False",
          "evaluation_data": {
            "input_output_pairs": [
              [
                "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]",
                "False"
              ]
            ],
            "original_function": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False"
          }
        }
      ]
    },
    "deduction_tasks": {
      "count": 24,
      "tasks": [
        {
          "task_id": "deduction_0",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False\n\n# Input:\n[3, 4, 5, 1, 2]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "True",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False",
            "test_input": "[3, 4, 5, 1, 2]",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False"
          }
        },
        {
          "task_id": "deduction_1",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False\n\n# Input:\n[1, 2, 3, 4, 5]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "True",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False",
            "test_input": "[1, 2, 3, 4, 5]",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False"
          }
        },
        {
          "task_id": "deduction_2",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False\n\n# Input:\n[5, 4, 3, 2, 1]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False",
            "test_input": "[5, 4, 3, 2, 1]",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False"
          }
        },
        {
          "task_id": "deduction_3",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False\n\n# Input:\n[1, 3, 5, 2, 4]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False",
            "test_input": "[1, 3, 5, 2, 4]",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False"
          }
        },
        {
          "task_id": "deduction_4",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False\n\n# Input:\n[1, 5, 3, 4, 2]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False",
            "test_input": "[1, 5, 3, 4, 2]",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False"
          }
        },
        {
          "task_id": "deduction_5",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False\n\n# Input:\n[]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "True",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False",
            "test_input": "[]",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False"
          }
        },
        {
          "task_id": "deduction_6",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True\n\n# Input:\n[3, 4, 5, 1, 2]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True",
            "test_input": "[3, 4, 5, 1, 2]",
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True"
          }
        },
        {
          "task_id": "deduction_7",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True\n\n# Input:\n[1, 2, 3, 4, 5]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True",
            "test_input": "[1, 2, 3, 4, 5]",
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True"
          }
        },
        {
          "task_id": "deduction_8",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True\n\n# Input:\n[5, 4, 3, 2, 1]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True",
            "test_input": "[5, 4, 3, 2, 1]",
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True"
          }
        },
        {
          "task_id": "deduction_9",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True\n\n# Input:\n[1, 3, 2, 4, 5]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True",
            "test_input": "[1, 3, 2, 4, 5]",
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True"
          }
        },
        {
          "task_id": "deduction_10",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True\n\n# Input:\n[1, 5, 4, 3, 2]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True",
            "test_input": "[1, 5, 4, 3, 2]",
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True"
          }
        },
        {
          "task_id": "deduction_11",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True\n\n# Input:\n[]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "True",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True",
            "test_input": "[]",
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True"
          }
        },
        {
          "task_id": "deduction_12",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True\n\n# Input:\n[3, 4, 5, 1, 2]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True",
            "test_input": "[3, 4, 5, 1, 2]",
            "original_function": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True"
          }
        },
        {
          "task_id": "deduction_13",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True\n\n# Input:\n[1, 2, 3, 4, 5]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "True",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True",
            "test_input": "[1, 2, 3, 4, 5]",
            "original_function": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True"
          }
        },
        {
          "task_id": "deduction_14",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True\n\n# Input:\n[5, 4, 3, 2, 1]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True",
            "test_input": "[5, 4, 3, 2, 1]",
            "original_function": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True"
          }
        },
        {
          "task_id": "deduction_15",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True\n\n# Input:\n[1, 2, 4, 3, 5]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True",
            "test_input": "[1, 2, 4, 3, 5]",
            "original_function": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True"
          }
        },
        {
          "task_id": "deduction_16",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True\n\n# Input:\n[1, 2, 3, 5, 4]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True",
            "test_input": "[1, 2, 3, 5, 4]",
            "original_function": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True"
          }
        },
        {
          "task_id": "deduction_17",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True\n\n# Input:\n[1, 2, 3, 4, 1]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True",
            "test_input": "[1, 2, 3, 4, 1]",
            "original_function": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True"
          }
        },
        {
          "task_id": "deduction_18",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False\n\n# Input:\n[3, 4, 5, 1, 2]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "True",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False",
            "test_input": "[3, 4, 5, 1, 2]",
            "original_function": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False"
          }
        },
        {
          "task_id": "deduction_19",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False\n\n# Input:\n[1, 2, 3, 4, 5]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False",
            "test_input": "[1, 2, 3, 4, 5]",
            "original_function": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False"
          }
        },
        {
          "task_id": "deduction_20",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False\n\n# Input:\n[5, 4, 3, 2, 1]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "True",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False",
            "test_input": "[5, 4, 3, 2, 1]",
            "original_function": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False"
          }
        },
        {
          "task_id": "deduction_21",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False\n\n# Input:\n[1, 3, 2, 4, 5]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "True",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False",
            "test_input": "[1, 3, 2, 4, 5]",
            "original_function": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False"
          }
        },
        {
          "task_id": "deduction_22",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False\n\n# Input:\n[1, 2, 3, 4, 1]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "True",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False",
            "test_input": "[1, 2, 3, 4, 1]",
            "original_function": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False"
          }
        },
        {
          "task_id": "deduction_23",
          "task_type": "deduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and specific input values. The Assistant must:\n\n1. **Privately think step-by-step** about how the code executes with the given inputs.  \n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.  \n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the output values—no labels, no comments, no extra text.  \n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **output rules**.\n\n# Output Rules:\n- If the output is a string, wrap it in quotes.  \n- For dicts, lists, and other literals, use valid Python literal notation.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False\n\n# Input:\n[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]\n\n# Assitant should follow this format:\n<think>\n# 1. Examine the code and input.  \n# 2. Walk through execution step by step.  \n# 3. Determine the exact output produced.\n</think>\n<answer>\n<your output here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "False",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False",
            "test_input": "[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]",
            "original_function": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False"
          }
        }
      ]
    },
    "abduction_tasks": {
      "count": 24,
      "tasks": [
        {
          "task_id": "abduction_0",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False\n\n# Observed Output:\nTrue\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([3, 4, 5, 1, 2])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False",
            "expected_output": "True",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False"
          }
        },
        {
          "task_id": "abduction_1",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False\n\n# Observed Output:\nTrue\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([1, 2, 3, 4, 5])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False",
            "expected_output": "True",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False"
          }
        },
        {
          "task_id": "abduction_2",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([5, 4, 3, 2, 1])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False",
            "expected_output": "False",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False"
          }
        },
        {
          "task_id": "abduction_3",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([1, 3, 5, 2, 4])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False",
            "expected_output": "False",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False"
          }
        },
        {
          "task_id": "abduction_4",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([1, 5, 3, 4, 2])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False",
            "expected_output": "False",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False"
          }
        },
        {
          "task_id": "abduction_5",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False\n\n# Observed Output:\nTrue\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False",
            "expected_output": "True",
            "original_function": "def move_one_ball(arr):\n    if not arr:\n        return True  # If the array is empty, return True\n\n    n = len(arr)\n    sorted_arr = sorted(arr)  # Create a sorted copy of the array\n\n    for i in range(n):\n        # Check if the array can be obtained by performing right shift operations\n        if arr == sorted_arr:\n            return True\n        arr = arr[1:] + [arr[0]]  # Perform right shift operation\n\n    return False"
          }
        },
        {
          "task_id": "abduction_6",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([3, 4, 5, 1, 2])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True",
            "expected_output": "False",
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True"
          }
        },
        {
          "task_id": "abduction_7",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([1, 2, 3, 4, 5])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True",
            "expected_output": "False",
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True"
          }
        },
        {
          "task_id": "abduction_8",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([5, 4, 3, 2, 1])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True",
            "expected_output": "False",
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True"
          }
        },
        {
          "task_id": "abduction_9",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([1, 3, 2, 4, 5])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True",
            "expected_output": "False",
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True"
          }
        },
        {
          "task_id": "abduction_10",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([1, 5, 4, 3, 2])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True",
            "expected_output": "False",
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True"
          }
        },
        {
          "task_id": "abduction_11",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True\n\n# Observed Output:\nTrue\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True",
            "expected_output": "True",
            "original_function": "def move_one_ball(arr):\n    \"\"\"\n    We have an array 'arr' of N integers arr[1], arr[2], ..., arr[N]. The\n    numbers in the array will be randomly ordered. Your task is to determine if\n    it is possible to get an array sorted in non-decreasing order by performing \n    the following operation on the given array:\n        You are allowed to perform right shift operation any number of times.\n    \n    One right shift operation means shifting all elements of the array by one\n    position in the right direction. The last element of the array will be moved to\n    the starting position in the array i.e. 0th index. \n\n    If it is possible to obtain the sorted array by performing the above operation\n    then return True else return False.\n    If the given array is empty then return True.\n\n    For Example:\n    \n    move_one_ball([3, 4, 5, 1, 2])==>True\n    Explanation: By performin 2 right shift operations, non-decreasing order can\n                 be achieved for the given array.\n    move_one_ball([3, 5, 4, 1, 2])==>False\n    Explanation:It is not possible to get non-decreasing order for the given\n                array by performing any number of right shift operations.\n    \"\"\"\n    # If the array is empty, return True\n    if not arr:\n        return True\n\n    # Create a copy of the array and rotate it once\n    rotated_arr = arr[1:] + [arr[0]]\n\n    # Check if the rotated array is sorted\n    for i in range(len(arr) - 1):\n        if rotated_arr[i] > rotated_arr[i + 1]:\n            return False\n\n    return True"
          }
        },
        {
          "task_id": "abduction_12",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([3, 4, 5, 1, 2])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True",
            "expected_output": "False",
            "original_function": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True"
          }
        },
        {
          "task_id": "abduction_13",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True\n\n# Observed Output:\nTrue\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([1, 2, 3, 4, 5])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True",
            "expected_output": "True",
            "original_function": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True"
          }
        },
        {
          "task_id": "abduction_14",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([5, 4, 3, 2, 1])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True",
            "expected_output": "False",
            "original_function": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True"
          }
        },
        {
          "task_id": "abduction_15",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([1, 2, 4, 3, 5])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True",
            "expected_output": "False",
            "original_function": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True"
          }
        },
        {
          "task_id": "abduction_16",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([1, 2, 3, 5, 4])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True",
            "expected_output": "False",
            "original_function": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True"
          }
        },
        {
          "task_id": "abduction_17",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([1, 2, 3, 4, 1])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True",
            "expected_output": "False",
            "original_function": "def move_one_ball(arr):\n    if not arr:  # If the array is empty, return True\n        return True\n\n    stack = []\n    for num in arr:\n        if stack and stack[-1] > num:\n            return False  # If the current number is less than the last number in the stack, return False\n        stack.append(num)\n\n    # Check if the array can be sorted by performing a single right shift\n    for i in range(1, len(arr)):\n        if arr[i] < arr[i-1]:\n            return False  # If any element is less than its previous element, return False\n\n    return True  # If all checks pass, return True"
          }
        },
        {
          "task_id": "abduction_18",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_triple_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False\n\n# Observed Output:\nTrue\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([3, 4, 5, 1, 2])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False",
            "expected_output": "True",
            "original_function": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False"
          }
        },
        {
          "task_id": "abduction_19",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([1, 2, 3, 4, 5])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False",
            "expected_output": "False",
            "original_function": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False"
          }
        },
        {
          "task_id": "abduction_20",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False\n\n# Observed Output:\nTrue\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([5, 4, 3, 2, 1])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False",
            "expected_output": "True",
            "original_function": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False"
          }
        },
        {
          "task_id": "abduction_21",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False\n\n# Observed Output:\nTrue\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([1, 3, 2, 4, 5])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False",
            "expected_output": "True",
            "original_function": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False"
          }
        },
        {
          "task_id": "abduction_22",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False\n\n# Observed Output:\nTrue\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([1, 2, 3, 4, 1])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False",
            "expected_output": "True",
            "original_function": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False"
          }
        },
        {
          "task_id": "abduction_23",
          "task_type": "abduction",
          "triple_id": "HumanEval/109_generated_0",
          "prompt": "\nA conversation between User and Assistant.  \nThe User provides a Python code snippet and its observed output. The Assistant must:\n\n1. **Privately think step-by-step** about which input produces that output.\n2. **Output exactly one** `<think>...</think>` block containing your full reasoning.\n3. **Then output exactly one** `<answer>...</answer>` block containing **only** the input values—no labels, no comments, no extra text.\n4. **Do not** generate any text outside these two blocks.\n5. Adhere to the **input rules**.\n\n# Input Rules:\n- If an argument is a string, wrap it in quotes.\n- For multiple arguments, separate by commas.\n- Use Python literal notation for lists, dicts, tuples.\n- Boolean values must be `True` or `False`.\n\nUser:\n# Python Code Snippet:\ndef move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False\n\n# Observed Output:\nFalse\n\n# Assitant should follow this format:\n\n# Example Response format:\n<think>\n# 1. Analyze the function signature.\n# 2. Walk through the code to see how the observed output arises.\n# 3. Identify specific input values that yield that output.\n</think>\n<answer>\n<your input here>\n</answer>\n\nAssistant:\n",
          "expected_solution": "move_one_ball([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])",
          "evaluation_data": {
            "function_code": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False",
            "expected_output": "False",
            "original_function": "def move_one_ball(arr):\n    if len(arr) == 0:\n        return True\n    for i in range(len(arr) - 1):\n        if arr[i] > arr[i + 1]:\n            return True\n    return False"
          }
        }
      ]
    },
    "total_tasks": 72,
    "timestamp": "2025-07-26T02:58:27.612033"
  }
]