{
  "scope": "Exact symbolic normalization and finite shape/resource checks for the authored constructor-rule JSON only. No OCaml extraction, Rocq proof, or complete catenable-deque certificate.",
  "input_sha256": "91fadc9f70c87bd86b5fc519f51d615129aa73ffaf4a95dcb165eb1258e6ecf4",
  "checker_sha256": "2731394b61de433dc034c144d6ca4d3268a1d75da2162de2fe564b6cadf7ea46",
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      "name": "rope_concat",
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      "r": 0,
      "A": 1,
      "coverage_cells": 1,
      "equations": [
        {
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          "index": 0,
          "normal_form": [
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              "x",
              0
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            [
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              "y",
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    {
      "name": "rope_duplicate",
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      "q_signature": 3,
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      "A": 1,
      "coverage_cells": 1,
      "equations": [
        {
          "rule": "share",
          "index": 0,
          "normal_form": [
            [
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              "x",
              0
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            [
              "variable",
              "x",
              0
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          ]
        }
      ]
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    {
      "name": "rope_rotate",
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      "r": 2,
      "A": 2,
      "coverage_cells": 63,
      "equations": [
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          "rule": "rotate",
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          "normal_form": [
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              "x",
              0
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            [
              "variable",
              "y",
              0
            ],
            [
              "variable",
              "z",
              0
            ]
          ]
        },
        {
          "rule": "top_Empty",
          "index": 0,
          "normal_form": []
        },
        {
          "rule": "top_A",
          "index": 0,
          "normal_form": [
            [
              "letter",
              "a"
            ]
          ]
        },
        {
          "rule": "top_B",
          "index": 0,
          "normal_form": [
            [
              "letter",
              "b"
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          ]
        },
        {
          "rule": "left_Empty",
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          "normal_form": [
            [
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              0
            ]
          ]
        },
        {
          "rule": "left_A",
          "index": 0,
          "normal_form": [
            [
              "letter",
              "a"
            ],
            [
              "variable",
              "z",
              0
            ]
          ]
        },
        {
          "rule": "left_B",
          "index": 0,
          "normal_form": [
            [
              "letter",
              "b"
            ],
            [
              "variable",
              "z",
              0
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          ]
        },
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          "rule": "left_Small",
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          "normal_form": [
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              "u0",
              0
            ],
            [
              "variable",
              "z",
              0
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          ]
        },
        {
          "rule": "left_Plug",
          "index": 0,
          "normal_form": [
            [
              "variable",
              "u0",
              0
            ],
            [
              "variable",
              "u1",
              0
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            [
              "variable",
              "u0",
              1
            ],
            [
              "variable",
              "z",
              0
            ]
          ]
        },
        {
          "rule": "top_Small",
          "index": 0,
          "normal_form": [
            [
              "variable",
              "u0",
              0
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          ]
        },
        {
          "rule": "top_Plug",
          "index": 0,
          "normal_form": [
            [
              "variable",
              "u0",
              0
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            [
              "variable",
              "u1",
              0
            ],
            [
              "variable",
              "u0",
              1
            ]
          ]
        }
      ]
    },
    {
      "name": "stack_init",
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      "q_signature": 3,
      "r": 0,
      "A": 1,
      "coverage_cells": 1,
      "equations": [
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          "rule": "init",
          "index": 0,
          "normal_form": []
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      ]
    },
    {
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      "A": 1,
      "coverage_cells": 1,
      "equations": [
        {
          "rule": "push",
          "index": 0,
          "normal_form": [
            [
              "letter",
              "a"
            ],
            [
              "variable",
              "x",
              0
            ]
          ]
        }
      ]
    },
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      "name": "stack_push_b",
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      "q_signature": 3,
      "r": 0,
      "A": 1,
      "coverage_cells": 1,
      "equations": [
        {
          "rule": "push",
          "index": 0,
          "normal_form": [
            [
              "letter",
              "b"
            ],
            [
              "variable",
              "x",
              0
            ]
          ]
        }
      ]
    },
    {
      "name": "stack_pop",
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      "q_signature": 3,
      "r": 1,
      "A": 0,
      "coverage_cells": 3,
      "equations": [
        {
          "rule": "nil",
          "index": 0,
          "normal_form": []
        },
        {
          "rule": "nil",
          "index": 1,
          "normal_form": []
        },
        {
          "rule": "a",
          "index": 0,
          "normal_form": [
            [
              "letter",
              "a"
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            [
              "variable",
              "x",
              0
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          ]
        },
        {
          "rule": "b",
          "index": 0,
          "normal_form": [
            [
              "letter",
              "b"
            ],
            [
              "variable",
              "x",
              0
            ]
          ]
        }
      ]
    },
    {
      "name": "context_compose",
      "status": "accepted",
      "q_signature": 3,
      "r": 0,
      "A": 1,
      "coverage_cells": 1,
      "equations": [
        {
          "rule": "compose",
          "index": 0,
          "normal_form": [
            [
              "variable",
              "k",
              0
            ],
            [
              "variable",
              "l",
              0
            ]
          ]
        },
        {
          "rule": "compose",
          "index": 1,
          "normal_form": [
            [
              "variable",
              "l",
              1
            ],
            [
              "variable",
              "k",
              1
            ]
          ]
        }
      ]
    },
    {
      "name": "context_plug",
      "status": "accepted",
      "q_signature": 3,
      "r": 0,
      "A": 1,
      "coverage_cells": 1,
      "equations": [
        {
          "rule": "plug",
          "index": 0,
          "normal_form": [
            [
              "variable",
              "k",
              0
            ],
            [
              "variable",
              "w",
              0
            ],
            [
              "variable",
              "k",
              1
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          ]
        }
      ]
    },
    {
      "name": "concat_boundary_algebra_only",
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      "q_signature": 3,
      "r": 0,
      "A": 4,
      "coverage_cells": 1,
      "equations": [
        {
          "rule": "move_suffix_to_child",
          "index": 0,
          "normal_form": [
            [
              "variable",
              "p",
              0
            ],
            [
              "variable",
              "c",
              0
            ],
            [
              "variable",
              "s",
              0
            ],
            [
              "variable",
              "y",
              0
            ],
            [
              "variable",
              "z",
              0
            ]
          ]
        }
      ]
    },
    {
      "name": "wrong_concat_order",
      "status": "rejected",
      "stage": "equation",
      "reason": "join equation 0: (('variable', 'y', 0), ('variable', 'x', 0)) != (('variable', 'x', 0), ('variable', 'y', 0))"
    },
    {
      "name": "allocation_understated",
      "status": "rejected",
      "stage": "resource",
      "reason": "A needs 1, declared 0"
    },
    {
      "name": "fresh_cycle",
      "status": "rejected",
      "stage": "shape",
      "reason": "ill-sorted, cyclic, or forward fresh reference"
    },
    {
      "name": "missing_pop_branch",
      "status": "rejected",
      "stage": "coverage",
      "reason": "truncated input cell matches 0 rules"
    },
    {
      "name": "overlapping_pop_rules",
      "status": "rejected",
      "stage": "coverage",
      "reason": "truncated input cell matches 2 rules"
    },
    {
      "name": "radius_understated",
      "status": "rejected",
      "stage": "resource",
      "reason": "r needs 1, declared 0"
    },
    {
      "name": "pop_retains_head",
      "status": "rejected",
      "stage": "equation",
      "reason": "a equation 0: (('letter', 'a'), ('variable', 'x', 0)) != (('letter', 'a'), ('letter', 'a'), ('variable', 'x', 0))"
    },
    {
      "name": "wrong_context_order",
      "status": "rejected",
      "stage": "equation",
      "reason": "compose equation 0: (('variable', 'l', 0), ('variable', 'k', 0)) != (('variable', 'k', 0), ('variable', 'l', 0))"
    },
    {
      "name": "valid_but_not_certified_erasure",
      "status": "rejected",
      "stage": "equation",
      "reason": "erase equation 0: () != (('variable', 'x', 0),)"
    }
  ]
}