{
  "scope": "exact minimization of six finite partial Moore systems with undefinedness observable; no infinite-state or scaffold proof",
  "claims_checked": {
    "fork_forward_residual_merges": true,
    "fork_two_way_residual_splits": true,
    "alternating_parity_is_partial_reversible": true,
    "restricted_tag_is_partial_reversible": true,
    "bounded_chain_is_partial_reversible": true,
    "presence_push_merges": true
  },
  "cases": [
    {
      "name": "fork_merge_forward",
      "reachable_source_states": 4,
      "residual_states": 3,
      "residual_blocks": [
        [
          "x0"
        ],
        [
          "x1"
        ],
        [
          "y0",
          "y1"
        ]
      ],
      "source_operations_partial_injective": true,
      "residual_operations_partial_injective": false,
      "residual_operations": {
        "+h": {
          "defined_arrows": [
            [
              "0",
              "2"
            ],
            [
              "1",
              "2"
            ]
          ],
          "partial_injective": false,
          "merge_witnesses": [
            {
              "target": "2",
              "sources": [
                "0",
                "1"
              ]
            }
          ]
        }
      },
      "source_merge_witnesses": {}
    },
    {
      "name": "fork_merge_two_way",
      "reachable_source_states": 4,
      "residual_states": 4,
      "residual_blocks": [
        [
          "x0"
        ],
        [
          "x1"
        ],
        [
          "y0"
        ],
        [
          "y1"
        ]
      ],
      "source_operations_partial_injective": true,
      "residual_operations_partial_injective": true,
      "residual_operations": {
        "+h": {
          "defined_arrows": [
            [
              "0",
              "2"
            ],
            [
              "1",
              "3"
            ]
          ],
          "partial_injective": true,
          "merge_witnesses": []
        },
        "-h": {
          "defined_arrows": [
            [
              "2",
              "0"
            ],
            [
              "3",
              "1"
            ]
          ],
          "partial_injective": true,
          "merge_witnesses": []
        }
      },
      "source_merge_witnesses": {}
    },
    {
      "name": "alternating_parity_restricted",
      "reachable_source_states": 4,
      "residual_states": 4,
      "residual_blocks": [
        [
          "b0"
        ],
        [
          "b1"
        ],
        [
          "q0"
        ],
        [
          "q1"
        ]
      ],
      "source_operations_partial_injective": true,
      "residual_operations_partial_injective": true,
      "residual_operations": {
        "+A": {
          "defined_arrows": [
            [
              "2",
              "0"
            ],
            [
              "3",
              "1"
            ]
          ],
          "partial_injective": true,
          "merge_witnesses": []
        },
        "-A": {
          "defined_arrows": [
            [
              "0",
              "2"
            ],
            [
              "1",
              "3"
            ]
          ],
          "partial_injective": true,
          "merge_witnesses": []
        },
        "+X": {
          "defined_arrows": [
            [
              "0",
              "3"
            ],
            [
              "1",
              "2"
            ]
          ],
          "partial_injective": true,
          "merge_witnesses": []
        },
        "-X": {
          "defined_arrows": [
            [
              "2",
              "1"
            ],
            [
              "3",
              "0"
            ]
          ],
          "partial_injective": true,
          "merge_witnesses": []
        }
      },
      "source_merge_witnesses": {}
    },
    {
      "name": "rightmost_tag_restricted",
      "reachable_source_states": 7,
      "residual_states": 7,
      "residual_blocks": [
        [
          "AB0"
        ],
        [
          "AB1"
        ],
        [
          "B0"
        ],
        [
          "B1"
        ],
        [
          "C0AB0"
        ],
        [
          "C1AB1"
        ],
        [
          "e"
        ]
      ],
      "source_operations_partial_injective": true,
      "residual_operations_partial_injective": true,
      "residual_operations": {
        "+B0": {
          "defined_arrows": [
            [
              "6",
              "2"
            ]
          ],
          "partial_injective": true,
          "merge_witnesses": []
        },
        "-B0": {
          "defined_arrows": [
            [
              "2",
              "6"
            ]
          ],
          "partial_injective": true,
          "merge_witnesses": []
        },
        "+B1": {
          "defined_arrows": [
            [
              "6",
              "3"
            ]
          ],
          "partial_injective": true,
          "merge_witnesses": []
        },
        "-B1": {
          "defined_arrows": [
            [
              "3",
              "6"
            ]
          ],
          "partial_injective": true,
          "merge_witnesses": []
        },
        "+A": {
          "defined_arrows": [
            [
              "2",
              "0"
            ],
            [
              "3",
              "1"
            ]
          ],
          "partial_injective": true,
          "merge_witnesses": []
        },
        "-A": {
          "defined_arrows": [
            [
              "0",
              "2"
            ],
            [
              "1",
              "3"
            ]
          ],
          "partial_injective": true,
          "merge_witnesses": []
        },
        "+C0": {
          "defined_arrows": [
            [
              "0",
              "4"
            ]
          ],
          "partial_injective": true,
          "merge_witnesses": []
        },
        "-C0": {
          "defined_arrows": [
            [
              "4",
              "0"
            ]
          ],
          "partial_injective": true,
          "merge_witnesses": []
        },
        "+C1": {
          "defined_arrows": [
            [
              "1",
              "5"
            ]
          ],
          "partial_injective": true,
          "merge_witnesses": []
        },
        "-C1": {
          "defined_arrows": [
            [
              "5",
              "1"
            ]
          ],
          "partial_injective": true,
          "merge_witnesses": []
        }
      },
      "source_merge_witnesses": {}
    },
    {
      "name": "bounded_depth_two_chain",
      "reachable_source_states": 3,
      "residual_states": 3,
      "residual_blocks": [
        [
          "X0"
        ],
        [
          "X1"
        ],
        [
          "X2"
        ]
      ],
      "source_operations_partial_injective": true,
      "residual_operations_partial_injective": true,
      "residual_operations": {
        "+X": {
          "defined_arrows": [
            [
              "0",
              "1"
            ],
            [
              "1",
              "2"
            ]
          ],
          "partial_injective": true,
          "merge_witnesses": []
        },
        "-X": {
          "defined_arrows": [
            [
              "1",
              "0"
            ],
            [
              "2",
              "1"
            ]
          ],
          "partial_injective": true,
          "merge_witnesses": []
        }
      },
      "source_merge_witnesses": {}
    },
    {
      "name": "presence_forward",
      "reachable_source_states": 2,
      "residual_states": 2,
      "residual_blocks": [
        [
          "absent"
        ],
        [
          "present"
        ]
      ],
      "source_operations_partial_injective": false,
      "residual_operations_partial_injective": false,
      "residual_operations": {
        "+X": {
          "defined_arrows": [
            [
              "0",
              "1"
            ],
            [
              "1",
              "1"
            ]
          ],
          "partial_injective": false,
          "merge_witnesses": [
            {
              "target": "1",
              "sources": [
                "0",
                "1"
              ]
            }
          ]
        }
      },
      "source_merge_witnesses": {
        "+X": [
          {
            "target": "present",
            "sources": [
              "absent",
              "present"
            ]
          }
        ]
      }
    }
  ]
}