YES
proof of /hpcwork/ff862203/termcomp26/benchmarks/lzrtV.pl
# AProVE Commit ID: 23a904c96b029b0a549cde0d0d17dbccf967db59 jckassing 20260626 unpublished dirty


Left Termination of the query pattern

g(a)

w.r.t. the given Prolog program could successfully be proven:

(0) Prolog
(1) PrologToIRSwTTransformerProof [SOUND, 26 ms]
(2) IRSwT
(3) IRSwTSimpleDependencyGraphProof [EQUIVALENT, 0 ms]
(4) TRUE


----------------------------------------

(0)
Obligation:
Clauses:

g(W) :- ','(eq(X, .(.(a, []), .(.(R, []), []))), ','(eq(Y, .(.(S, .(c, [])), .([], []))), ','(app_1(X, Y, Z), ','(eq(Z, .(U, V)), app_2(U, U, W))))).
app_1([], X, X).
app_1(.(X, Xs), Ys, .(X, Zs)) :- app_1(Xs, Ys, Zs).
app_2([], X, X).
app_2(.(X, Xs), Ys, .(X, Zs)) :- app_2(Xs, Ys, Zs).
eq(X, X).


Query: g(a)
----------------------------------------

(1) PrologToIRSwTTransformerProof (SOUND)
Transformed Prolog program to IRSwT according to method in Master Thesis of A. Weinert

{
    "root": 1,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(g W)",
                "(',' (eq X (. (. (a) ([])) (. (. R ([])) ([])))) (',' (eq Y (. (. S (. (c) ([]))) (. ([]) ([])))) (',' (app_1 X Y Z) (',' (eq Z (. U V)) (app_2 U U W)))))"
            ],
            [
                "(app_1 ([]) X X)",
                null
            ],
            [
                "(app_1 (. X Xs) Ys (. X Zs))",
                "(app_1 Xs Ys Zs)"
            ],
            [
                "(app_2 ([]) X X)",
                null
            ],
            [
                "(app_2 (. X Xs) Ys (. X Zs))",
                "(app_2 Xs Ys Zs)"
            ],
            [
                "(eq X X)",
                null
            ]
        ]
    },
    "graph": {
        "nodes": {
            "type": "Nodes",
            "475": {
                "goal": [
                    {
                        "clause": 3,
                        "scope": 10,
                        "term": "(app_2 T51 (. T53 (. T54 T51)) T52)"
                    },
                    {
                        "clause": 4,
                        "scope": 10,
                        "term": "(app_2 T51 (. T53 (. T54 T51)) T52)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "476": {
                "goal": [{
                    "clause": 3,
                    "scope": 10,
                    "term": "(app_2 T51 (. T53 (. T54 T51)) T52)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "477": {
                "goal": [{
                    "clause": 4,
                    "scope": 10,
                    "term": "(app_2 T51 (. T53 (. T54 T51)) T52)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "598": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
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                    "exprvars": []
                }
            },
            "478": {
                "goal": [{
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                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
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                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "599": {
                "goal": [],
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            },
            "479": {
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                }
            },
            "480": {
                "goal": [],
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                        "relations": []
                    },
                    "ground": [],
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                }
            },
            "481": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(app_2 T84 (. T86 (. T87 (. T88 T84))) T85)"
                }],
                "kb": {
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            },
            "482": {
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                    "ground": [],
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                }
            },
            "483": {
                "goal": [
                    {
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                        "term": "(app_2 T84 (. T86 (. T87 (. T88 T84))) T85)"
                    },
                    {
                        "clause": 4,
                        "scope": 11,
                        "term": "(app_2 T84 (. T86 (. T87 (. T88 T84))) T85)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
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                    },
                    "ground": [],
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                }
            },
            "484": {
                "goal": [{
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                    "scope": 11,
                    "term": "(app_2 T84 (. T86 (. T87 (. T88 T84))) T85)"
                }],
                "kb": {
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                    "arithmetic": {
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                        "relations": []
                    },
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                }
            },
            "1": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(g T1)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
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                }
            },
            "485": {
                "goal": [{
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                    "term": "(app_2 T84 (. T86 (. T87 (. T88 T84))) T85)"
                }],
                "kb": {
                    "nonunifying": [],
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                    },
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            },
            "2": {
                "goal": [{
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                    "scope": 1,
                    "term": "(g T1)"
                }],
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                        "type": "PlainIntegerRelationState",
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                    },
                    "ground": [],
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                }
            },
            "486": {
                "goal": [{
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                    "scope": -1,
                    "term": "(true)"
                }],
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            },
            "487": {
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                }
            },
            "400": {
                "goal": [
                    {
                        "clause": 1,
                        "scope": 5,
                        "term": "(app_1 (. (. X75 ([])) ([])) (. (. X76 (. (c) ([]))) (. ([]) ([]))) X77)"
                    },
                    {
                        "clause": 2,
                        "scope": 5,
                        "term": "(app_1 (. (. X75 ([])) ([])) (. (. X76 (. (c) ([]))) (. ([]) ([]))) X77)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": ["X77"],
                    "exprvars": []
                }
            },
            "488": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "401": {
                "goal": [{
                    "clause": 2,
                    "scope": 5,
                    "term": "(app_1 (. (. X75 ([])) ([])) (. (. X76 (. (c) ([]))) (. ([]) ([]))) X77)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": ["X77"],
                    "exprvars": []
                }
            },
            "489": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(app_2 T128 (. T130 (. T131 (. T132 (. T133 T128)))) T129)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
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                    "exprvars": []
                }
            },
            "7": {
                "goal": [{
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                    "scope": -1,
                    "term": "(',' (eq X15 (. (. (a) ([])) (. (. X16 ([])) ([])))) (',' (eq X17 (. (. X18 (. (c) ([]))) (. ([]) ([])))) (',' (app_1 X15 X17 X19) (',' (eq X19 (. X20 X21)) (app_2 X20 X20 T6)))))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [
                        "X15",
                        "X16",
                        "X17",
                        "X18",
                        "X19",
                        "X20",
                        "X21"
                    ],
                    "exprvars": []
                }
            },
            "528": {
                "goal": [{
                    "clause": 3,
                    "scope": 13,
                    "term": "(app_2 T183 (. T185 (. T186 (. T187 (. T188 (. T189 T183))))) T184)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "408": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(app_1 ([]) (. (. X102 (. (c) ([]))) (. ([]) ([]))) X103)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
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                        "type": "PlainIntegerRelationState",
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                    "ground": [],
                    "free": ["X103"],
                    "exprvars": []
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            },
            "529": {
                "goal": [{
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                    "term": "(app_2 T183 (. T185 (. T186 (. T187 (. T188 (. T189 T183))))) T184)"
                }],
                "kb": {
                    "nonunifying": [],
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                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
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            },
            "409": {
                "goal": [
                    {
                        "clause": 1,
                        "scope": 6,
                        "term": "(app_1 ([]) (. (. X102 (. (c) ([]))) (. ([]) ([]))) X103)"
                    },
                    {
                        "clause": 2,
                        "scope": 6,
                        "term": "(app_1 ([]) (. (. X102 (. (c) ([]))) (. ([]) ([]))) X103)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
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                    },
                    "ground": [],
                    "free": ["X103"],
                    "exprvars": []
                }
            },
            "490": {
                "goal": [],
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                        "type": "PlainIntegerRelationState",
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            },
            "491": {
                "goal": [
                    {
                        "clause": 3,
                        "scope": 12,
                        "term": "(app_2 T128 (. T130 (. T131 (. T132 (. T133 T128)))) T129)"
                    },
                    {
                        "clause": 4,
                        "scope": 12,
                        "term": "(app_2 T128 (. T130 (. T131 (. T132 (. T133 T128)))) T129)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
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                    "ground": [],
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            },
            "371": {
                "goal": [{
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                    "scope": -1,
                    "term": "(',' (eq X17 (. (. X18 (. (c) ([]))) (. ([]) ([])))) (',' (app_1 (. (. (a) ([])) (. (. X36 ([])) ([]))) X17 X19) (',' (eq X19 (. X20 X21)) (app_2 X20 X20 T6))))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [
                        "X17",
                        "X18",
                        "X19",
                        "X20",
                        "X21"
                    ],
                    "exprvars": []
                }
            },
            "492": {
                "goal": [{
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                    "scope": 12,
                    "term": "(app_2 T128 (. T130 (. T131 (. T132 (. T133 T128)))) T129)"
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                "kb": {
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            "372": {
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                    "term": "(',' (eq X17 (. (. X18 (. (c) ([]))) (. ([]) ([])))) (',' (app_1 (. (. (a) ([])) (. (. X36 ([])) ([]))) X17 X19) (',' (eq X19 (. X20 X21)) (app_2 X20 X20 T6))))"
                }],
                "kb": {
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                        "X19",
                        "X20",
                        "X21"
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                    "exprvars": []
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            },
            "493": {
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                    "term": "(app_2 T128 (. T130 (. T131 (. T132 (. T133 T128)))) T129)"
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            "494": {
                "goal": [{
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                    "term": "(true)"
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            "495": {
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            "496": {
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            "410": {
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                    "term": "(app_1 ([]) (. (. X102 (. (c) ([]))) (. ([]) ([]))) X103)"
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            },
            "498": {
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            },
            "378": {
                "goal": [{
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                    "exprvars": []
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            },
            "411": {
                "goal": [{
                    "clause": 2,
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                    "term": "(app_1 ([]) (. (. X102 (. (c) ([]))) (. ([]) ([]))) X103)"
                }],
                "kb": {
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            },
            "499": {
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                    },
                    {
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                        "term": "(app_2 T183 (. T185 (. T186 (. T187 (. T188 (. T189 T183))))) T184)"
                    }
                ],
                "kb": {
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            "412": {
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            "533": {
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            },
            "534": {
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            },
            "414": {
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            },
            "535": {
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            },
            "415": {
                "goal": [{
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                    "scope": 7,
                    "term": "(',' (eq T7 (. X20 X21)) (app_2 X20 X20 T8))"
                }],
                "kb": {
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                    "arithmetic": {
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                        "relations": []
                    },
                    "ground": [],
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                        "X21"
                    ],
                    "exprvars": []
                }
            },
            "416": {
                "goal": [{
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                    "scope": -1,
                    "term": "(app_2 T18 T18 T19)"
                }],
                "kb": {
                    "nonunifying": [],
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                        "type": "PlainIntegerRelationState",
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                    },
                    "ground": [],
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            },
            "417": {
                "goal": [],
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                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
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                    "exprvars": []
                }
            },
            "418": {
                "goal": [
                    {
                        "clause": 3,
                        "scope": 8,
                        "term": "(app_2 T18 T18 T19)"
                    },
                    {
                        "clause": 4,
                        "scope": 8,
                        "term": "(app_2 T18 T18 T19)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
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                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
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                    "ground": [],
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            },
            "419": {
                "goal": [{
                    "clause": 3,
                    "scope": 8,
                    "term": "(app_2 T18 T18 T19)"
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                "kb": {
                    "nonunifying": [],
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                        "type": "PlainIntegerRelationState",
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                    },
                    "ground": [],
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            },
            "382": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(app_1 (. (. (a) ([])) (. (. X36 ([])) ([]))) (. (. X49 (. (c) ([]))) (. ([]) ([]))) X19)"
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                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": ["X19"],
                    "exprvars": []
                }
            },
            "383": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(',' (eq T7 (. X20 X21)) (app_2 X20 X20 T8))"
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                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [
                        "X20",
                        "X21"
                    ],
                    "exprvars": []
                }
            },
            "385": {
                "goal": [
                    {
                        "clause": 1,
                        "scope": 4,
                        "term": "(app_1 (. (. (a) ([])) (. (. X36 ([])) ([]))) (. (. X49 (. (c) ([]))) (. ([]) ([]))) X19)"
                    },
                    {
                        "clause": 2,
                        "scope": 4,
                        "term": "(app_1 (. (. (a) ([])) (. (. X36 ([])) ([]))) (. (. X49 (. (c) ([]))) (. ([]) ([]))) X19)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": ["X19"],
                    "exprvars": []
                }
            },
            "387": {
                "goal": [{
                    "clause": 2,
                    "scope": 4,
                    "term": "(app_1 (. (. (a) ([])) (. (. X36 ([])) ([]))) (. (. X49 (. (c) ([]))) (. ([]) ([]))) X19)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": ["X19"],
                    "exprvars": []
                }
            },
            "420": {
                "goal": [{
                    "clause": 4,
                    "scope": 8,
                    "term": "(app_2 T18 T18 T19)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "421": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
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                    "exprvars": []
                }
            },
            "422": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "664": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(app_2 T470 (. T472 T473) T471)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "423": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "665": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "424": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(app_2 T29 (. T31 T29) T30)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "425": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "426": {
                "goal": [
                    {
                        "clause": 3,
                        "scope": 9,
                        "term": "(app_2 T29 (. T31 T29) T30)"
                    },
                    {
                        "clause": 4,
                        "scope": 9,
                        "term": "(app_2 T29 (. T31 T29) T30)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "547": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(app_2 T249 (. T251 (. T252 (. T253 (. T254 (. T255 (. T256 T249)))))) T250)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "427": {
                "goal": [{
                    "clause": 3,
                    "scope": 9,
                    "term": "(app_2 T29 (. T31 T29) T30)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "548": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "428": {
                "goal": [{
                    "clause": 4,
                    "scope": 9,
                    "term": "(app_2 T29 (. T31 T29) T30)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "429": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "430": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "431": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "399": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(app_1 (. (. X75 ([])) ([])) (. (. X76 (. (c) ([]))) (. ([]) ([]))) X77)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": ["X77"],
                    "exprvars": []
                }
            },
            "432": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(app_2 T51 (. T53 (. T54 T51)) T52)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "433": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "562": {
                "goal": [
                    {
                        "clause": 3,
                        "scope": 14,
                        "term": "(app_2 T249 (. T251 (. T252 (. T253 (. T254 (. T255 (. T256 T249)))))) T250)"
                    },
                    {
                        "clause": 4,
                        "scope": 14,
                        "term": "(app_2 T249 (. T251 (. T252 (. T253 (. T254 (. T255 (. T256 T249)))))) T250)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "566": {
                "goal": [{
                    "clause": 3,
                    "scope": 14,
                    "term": "(app_2 T249 (. T251 (. T252 (. T253 (. T254 (. T255 (. T256 T249)))))) T250)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "567": {
                "goal": [{
                    "clause": 4,
                    "scope": 14,
                    "term": "(app_2 T249 (. T251 (. T252 (. T253 (. T254 (. T255 (. T256 T249)))))) T250)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "600": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "601": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(app_2 T414 (. T416 (. T417 (. T418 (. T419 (. T420 (. T421 (. T422 (. T423 T414)))))))) T415)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "602": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "603": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(app_2 T414 (. T416 T440) T415)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "570": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "571": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "572": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "574": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(app_2 T326 (. T328 (. T329 (. T330 (. T331 (. T332 (. T333 (. T334 T326))))))) T327)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "575": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "615": {
                "goal": [
                    {
                        "clause": 3,
                        "scope": 16,
                        "term": "(app_2 T414 (. T416 T440) T415)"
                    },
                    {
                        "clause": 4,
                        "scope": 16,
                        "term": "(app_2 T414 (. T416 T440) T415)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "616": {
                "goal": [{
                    "clause": 3,
                    "scope": 16,
                    "term": "(app_2 T414 (. T416 T440) T415)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "617": {
                "goal": [{
                    "clause": 4,
                    "scope": 16,
                    "term": "(app_2 T414 (. T416 T440) T415)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "581": {
                "goal": [
                    {
                        "clause": 3,
                        "scope": 15,
                        "term": "(app_2 T326 (. T328 (. T329 (. T330 (. T331 (. T332 (. T333 (. T334 T326))))))) T327)"
                    },
                    {
                        "clause": 4,
                        "scope": 15,
                        "term": "(app_2 T326 (. T328 (. T329 (. T330 (. T331 (. T332 (. T333 (. T334 T326))))))) T327)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "585": {
                "goal": [{
                    "clause": 3,
                    "scope": 15,
                    "term": "(app_2 T326 (. T328 (. T329 (. T330 (. T331 (. T332 (. T333 (. T334 T326))))))) T327)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "586": {
                "goal": [{
                    "clause": 4,
                    "scope": 15,
                    "term": "(app_2 T326 (. T328 (. T329 (. T330 (. T331 (. T332 (. T333 (. T334 T326))))))) T327)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "620": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "621": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "347": {
                "goal": [{
                    "clause": 5,
                    "scope": 2,
                    "term": "(',' (eq X15 (. (. (a) ([])) (. (. X16 ([])) ([])))) (',' (eq X17 (. (. X18 (. (c) ([]))) (. ([]) ([])))) (',' (app_1 X15 X17 X19) (',' (eq X19 (. X20 X21)) (app_2 X20 X20 T6)))))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [
                        "X15",
                        "X16",
                        "X17",
                        "X18",
                        "X19",
                        "X20",
                        "X21"
                    ],
                    "exprvars": []
                }
            },
            "627": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            }
        },
        "edges": [
            {
                "from": 1,
                "to": 2,
                "label": "CASE"
            },
            {
                "from": 2,
                "to": 7,
                "label": "ONLY EVAL with clause\ng(X14) :- ','(eq(X15, .(.(a, []), .(.(X16, []), []))), ','(eq(X17, .(.(X18, .(c, [])), .([], []))), ','(app_1(X15, X17, X19), ','(eq(X19, .(X20, X21)), app_2(X20, X20, X14))))).\nand substitutionT1 -> T6,\nX14 -> T6,\nT5 -> T6"
            },
            {
                "from": 7,
                "to": 347,
                "label": "CASE"
            },
            {
                "from": 347,
                "to": 371,
                "label": "ONLY EVAL with clause\neq(X34, X34).\nand substitutionX15 -> .(.(a, []), .(.(X36, []), [])),\nX34 -> .(.(a, []), .(.(X36, []), [])),\nX16 -> X36,\nX35 -> .(.(a, []), .(.(X36, []), []))"
            },
            {
                "from": 371,
                "to": 372,
                "label": "CASE"
            },
            {
                "from": 372,
                "to": 378,
                "label": "ONLY EVAL with clause\neq(X47, X47).\nand substitutionX17 -> .(.(X49, .(c, [])), .([], [])),\nX47 -> .(.(X49, .(c, [])), .([], [])),\nX18 -> X49,\nX48 -> .(.(X49, .(c, [])), .([], []))"
            },
            {
                "from": 378,
                "to": 382,
                "label": "SPLIT 1"
            },
            {
                "from": 378,
                "to": 383,
                "label": "SPLIT 2\nreplacements:X19 -> T7,\nT6 -> T8"
            },
            {
                "from": 382,
                "to": 385,
                "label": "CASE"
            },
            {
                "from": 383,
                "to": 415,
                "label": "CASE"
            },
            {
                "from": 385,
                "to": 387,
                "label": "BACKTRACK\nfor clause: app_1([], X, X)because of non-unification"
            },
            {
                "from": 387,
                "to": 399,
                "label": "ONLY EVAL with clause\napp_1(.(X71, X72), X73, .(X71, X74)) :- app_1(X72, X73, X74).\nand substitutionX71 -> .(a, []),\nX36 -> X75,\nX72 -> .(.(X75, []), []),\nX49 -> X76,\nX73 -> .(.(X76, .(c, [])), .([], [])),\nX74 -> X77,\nX19 -> .(.(a, []), X77)"
            },
            {
                "from": 399,
                "to": 400,
                "label": "CASE"
            },
            {
                "from": 400,
                "to": 401,
                "label": "BACKTRACK\nfor clause: app_1([], X, X)because of non-unification"
            },
            {
                "from": 401,
                "to": 408,
                "label": "ONLY EVAL with clause\napp_1(.(X97, X98), X99, .(X97, X100)) :- app_1(X98, X99, X100).\nand substitutionX75 -> X101,\nX97 -> .(X101, []),\nX98 -> [],\nX76 -> X102,\nX99 -> .(.(X102, .(c, [])), .([], [])),\nX100 -> X103,\nX77 -> .(.(X101, []), X103)"
            },
            {
                "from": 408,
                "to": 409,
                "label": "CASE"
            },
            {
                "from": 409,
                "to": 410,
                "label": "PARALLEL"
            },
            {
                "from": 409,
                "to": 411,
                "label": "PARALLEL"
            },
            {
                "from": 410,
                "to": 412,
                "label": "ONLY EVAL with clause\napp_1([], X114, X114).\nand substitutionX102 -> X115,\nX114 -> .(.(X115, .(c, [])), .([], [])),\nX103 -> .(.(X115, .(c, [])), .([], []))"
            },
            {
                "from": 411,
                "to": 414,
                "label": "BACKTRACK\nfor clause: app_1(.(X, Xs), Ys, .(X, Zs)) :- app_1(Xs, Ys, Zs)because of non-unification"
            },
            {
                "from": 412,
                "to": 413,
                "label": "SUCCESS"
            },
            {
                "from": 415,
                "to": 416,
                "label": "EVAL with clause\neq(X124, X124).\nand substitutionT7 -> .(T18, T17),\nX124 -> .(T18, T17),\nX20 -> T18,\nX21 -> T17,\nT15 -> .(T18, T17),\nT16 -> T18,\nT8 -> T19"
            },
            {
                "from": 415,
                "to": 417,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 416,
                "to": 418,
                "label": "CASE"
            },
            {
                "from": 418,
                "to": 419,
                "label": "PARALLEL"
            },
            {
                "from": 418,
                "to": 420,
                "label": "PARALLEL"
            },
            {
                "from": 419,
                "to": 421,
                "label": "EVAL with clause\napp_2([], X131, X131).\nand substitutionT18 -> [],\nX131 -> [],\nT19 -> []"
            },
            {
                "from": 419,
                "to": 422,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 420,
                "to": 424,
                "label": "EVAL with clause\napp_2(.(X140, X141), X142, .(X140, X143)) :- app_2(X141, X142, X143).\nand substitutionX140 -> T31,\nX141 -> T29,\nT18 -> .(T31, T29),\nX142 -> .(T31, T29),\nX143 -> T30,\nT19 -> .(T31, T30),\nT27 -> T29,\nT28 -> T30,\nT26 -> T31"
            },
            {
                "from": 420,
                "to": 425,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 421,
                "to": 423,
                "label": "SUCCESS"
            },
            {
                "from": 424,
                "to": 426,
                "label": "CASE"
            },
            {
                "from": 426,
                "to": 427,
                "label": "PARALLEL"
            },
            {
                "from": 426,
                "to": 428,
                "label": "PARALLEL"
            },
            {
                "from": 427,
                "to": 429,
                "label": "EVAL with clause\napp_2([], X150, X150).\nand substitutionT29 -> [],\nT31 -> T38,\nX150 -> .(T38, []),\nT30 -> .(T38, [])"
            },
            {
                "from": 427,
                "to": 430,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 428,
                "to": 432,
                "label": "EVAL with clause\napp_2(.(X159, X160), X161, .(X159, X162)) :- app_2(X160, X161, X162).\nand substitutionX159 -> T54,\nX160 -> T51,\nT29 -> .(T54, T51),\nT31 -> T53,\nX161 -> .(T53, .(T54, T51)),\nX162 -> T52,\nT30 -> .(T54, T52),\nT48 -> T51,\nT50 -> T52,\nT49 -> T53,\nT47 -> T54"
            },
            {
                "from": 428,
                "to": 433,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 429,
                "to": 431,
                "label": "SUCCESS"
            },
            {
                "from": 432,
                "to": 475,
                "label": "CASE"
            },
            {
                "from": 475,
                "to": 476,
                "label": "PARALLEL"
            },
            {
                "from": 475,
                "to": 477,
                "label": "PARALLEL"
            },
            {
                "from": 476,
                "to": 478,
                "label": "EVAL with clause\napp_2([], X169, X169).\nand substitutionT51 -> [],\nT53 -> T67,\nT54 -> T68,\nX169 -> .(T67, .(T68, [])),\nT52 -> .(T67, .(T68, []))"
            },
            {
                "from": 476,
                "to": 479,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 477,
                "to": 481,
                "label": "EVAL with clause\napp_2(.(X178, X179), X180, .(X178, X181)) :- app_2(X179, X180, X181).\nand substitutionX178 -> T88,\nX179 -> T84,\nT51 -> .(T88, T84),\nT53 -> T86,\nT54 -> T87,\nX180 -> .(T86, .(T87, .(T88, T84))),\nX181 -> T85,\nT52 -> .(T88, T85),\nT80 -> T84,\nT83 -> T85,\nT81 -> T86,\nT82 -> T87,\nT79 -> T88"
            },
            {
                "from": 477,
                "to": 482,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 478,
                "to": 480,
                "label": "SUCCESS"
            },
            {
                "from": 481,
                "to": 483,
                "label": "CASE"
            },
            {
                "from": 483,
                "to": 484,
                "label": "PARALLEL"
            },
            {
                "from": 483,
                "to": 485,
                "label": "PARALLEL"
            },
            {
                "from": 484,
                "to": 486,
                "label": "EVAL with clause\napp_2([], X188, X188).\nand substitutionT84 -> [],\nT86 -> T107,\nT87 -> T108,\nT88 -> T109,\nX188 -> .(T107, .(T108, .(T109, []))),\nT85 -> .(T107, .(T108, .(T109, [])))"
            },
            {
                "from": 484,
                "to": 487,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 485,
                "to": 489,
                "label": "EVAL with clause\napp_2(.(X197, X198), X199, .(X197, X200)) :- app_2(X198, X199, X200).\nand substitutionX197 -> T133,\nX198 -> T128,\nT84 -> .(T133, T128),\nT86 -> T130,\nT87 -> T131,\nT88 -> T132,\nX199 -> .(T130, .(T131, .(T132, .(T133, T128)))),\nX200 -> T129,\nT85 -> .(T133, T129),\nT123 -> T128,\nT127 -> T129,\nT124 -> T130,\nT125 -> T131,\nT126 -> T132,\nT122 -> T133"
            },
            {
                "from": 485,
                "to": 490,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 486,
                "to": 488,
                "label": "SUCCESS"
            },
            {
                "from": 489,
                "to": 491,
                "label": "CASE"
            },
            {
                "from": 491,
                "to": 492,
                "label": "PARALLEL"
            },
            {
                "from": 491,
                "to": 493,
                "label": "PARALLEL"
            },
            {
                "from": 492,
                "to": 494,
                "label": "EVAL with clause\napp_2([], X207, X207).\nand substitutionT128 -> [],\nT130 -> T158,\nT131 -> T159,\nT132 -> T160,\nT133 -> T161,\nX207 -> .(T158, .(T159, .(T160, .(T161, [])))),\nT129 -> .(T158, .(T159, .(T160, .(T161, []))))"
            },
            {
                "from": 492,
                "to": 495,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 493,
                "to": 497,
                "label": "EVAL with clause\napp_2(.(X216, X217), X218, .(X216, X219)) :- app_2(X217, X218, X219).\nand substitutionX216 -> T189,\nX217 -> T183,\nT128 -> .(T189, T183),\nT130 -> T185,\nT131 -> T186,\nT132 -> T187,\nT133 -> T188,\nX218 -> .(T185, .(T186, .(T187, .(T188, .(T189, T183))))),\nX219 -> T184,\nT129 -> .(T189, T184),\nT177 -> T183,\nT182 -> T184,\nT178 -> T185,\nT179 -> T186,\nT180 -> T187,\nT181 -> T188,\nT176 -> T189"
            },
            {
                "from": 493,
                "to": 498,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 494,
                "to": 496,
                "label": "SUCCESS"
            },
            {
                "from": 497,
                "to": 499,
                "label": "CASE"
            },
            {
                "from": 499,
                "to": 528,
                "label": "PARALLEL"
            },
            {
                "from": 499,
                "to": 529,
                "label": "PARALLEL"
            },
            {
                "from": 528,
                "to": 533,
                "label": "EVAL with clause\napp_2([], X226, X226).\nand substitutionT183 -> [],\nT185 -> T220,\nT186 -> T221,\nT187 -> T222,\nT188 -> T223,\nT189 -> T224,\nX226 -> .(T220, .(T221, .(T222, .(T223, .(T224, []))))),\nT184 -> .(T220, .(T221, .(T222, .(T223, .(T224, [])))))"
            },
            {
                "from": 528,
                "to": 534,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 529,
                "to": 547,
                "label": "EVAL with clause\napp_2(.(X235, X236), X237, .(X235, X238)) :- app_2(X236, X237, X238).\nand substitutionX235 -> T256,\nX236 -> T249,\nT183 -> .(T256, T249),\nT185 -> T251,\nT186 -> T252,\nT187 -> T253,\nT188 -> T254,\nT189 -> T255,\nX237 -> .(T251, .(T252, .(T253, .(T254, .(T255, .(T256, T249)))))),\nX238 -> T250,\nT184 -> .(T256, T250),\nT242 -> T249,\nT248 -> T250,\nT243 -> T251,\nT244 -> T252,\nT245 -> T253,\nT246 -> T254,\nT247 -> T255,\nT241 -> T256"
            },
            {
                "from": 529,
                "to": 548,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 533,
                "to": 535,
                "label": "SUCCESS"
            },
            {
                "from": 547,
                "to": 562,
                "label": "CASE"
            },
            {
                "from": 562,
                "to": 566,
                "label": "PARALLEL"
            },
            {
                "from": 562,
                "to": 567,
                "label": "PARALLEL"
            },
            {
                "from": 566,
                "to": 570,
                "label": "EVAL with clause\napp_2([], X245, X245).\nand substitutionT249 -> [],\nT251 -> T293,\nT252 -> T294,\nT253 -> T295,\nT254 -> T296,\nT255 -> T297,\nT256 -> T298,\nX245 -> .(T293, .(T294, .(T295, .(T296, .(T297, .(T298, [])))))),\nT250 -> .(T293, .(T294, .(T295, .(T296, .(T297, .(T298, []))))))"
            },
            {
                "from": 566,
                "to": 571,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 567,
                "to": 574,
                "label": "EVAL with clause\napp_2(.(X254, X255), X256, .(X254, X257)) :- app_2(X255, X256, X257).\nand substitutionX254 -> T334,\nX255 -> T326,\nT249 -> .(T334, T326),\nT251 -> T328,\nT252 -> T329,\nT253 -> T330,\nT254 -> T331,\nT255 -> T332,\nT256 -> T333,\nX256 -> .(T328, .(T329, .(T330, .(T331, .(T332, .(T333, .(T334, T326))))))),\nX257 -> T327,\nT250 -> .(T334, T327),\nT318 -> T326,\nT325 -> T327,\nT319 -> T328,\nT320 -> T329,\nT321 -> T330,\nT322 -> T331,\nT323 -> T332,\nT324 -> T333,\nT317 -> T334"
            },
            {
                "from": 567,
                "to": 575,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 570,
                "to": 572,
                "label": "SUCCESS"
            },
            {
                "from": 574,
                "to": 581,
                "label": "CASE"
            },
            {
                "from": 581,
                "to": 585,
                "label": "PARALLEL"
            },
            {
                "from": 581,
                "to": 586,
                "label": "PARALLEL"
            },
            {
                "from": 585,
                "to": 598,
                "label": "EVAL with clause\napp_2([], X264, X264).\nand substitutionT326 -> [],\nT328 -> T377,\nT329 -> T378,\nT330 -> T379,\nT331 -> T380,\nT332 -> T381,\nT333 -> T382,\nT334 -> T383,\nX264 -> .(T377, .(T378, .(T379, .(T380, .(T381, .(T382, .(T383, []))))))),\nT327 -> .(T377, .(T378, .(T379, .(T380, .(T381, .(T382, .(T383, [])))))))"
            },
            {
                "from": 585,
                "to": 599,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 586,
                "to": 601,
                "label": "EVAL with clause\napp_2(.(X273, X274), X275, .(X273, X276)) :- app_2(X274, X275, X276).\nand substitutionX273 -> T423,\nX274 -> T414,\nT326 -> .(T423, T414),\nT328 -> T416,\nT329 -> T417,\nT330 -> T418,\nT331 -> T419,\nT332 -> T420,\nT333 -> T421,\nT334 -> T422,\nX275 -> .(T416, .(T417, .(T418, .(T419, .(T420, .(T421, .(T422, .(T423, T414)))))))),\nX276 -> T415,\nT327 -> .(T423, T415),\nT405 -> T414,\nT413 -> T415,\nT406 -> T416,\nT407 -> T417,\nT408 -> T418,\nT409 -> T419,\nT410 -> T420,\nT411 -> T421,\nT412 -> T422,\nT404 -> T423"
            },
            {
                "from": 586,
                "to": 602,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 598,
                "to": 600,
                "label": "SUCCESS"
            },
            {
                "from": 601,
                "to": 603,
                "label": "GENERALIZATION\nT440 <-- .(T417, .(T418, .(T419, .(T420, .(T421, .(T422, .(T423, T414)))))))"
            },
            {
                "from": 603,
                "to": 615,
                "label": "CASE"
            },
            {
                "from": 615,
                "to": 616,
                "label": "PARALLEL"
            },
            {
                "from": 615,
                "to": 617,
                "label": "PARALLEL"
            },
            {
                "from": 616,
                "to": 620,
                "label": "EVAL with clause\napp_2([], X285, X285).\nand substitutionT414 -> [],\nT416 -> T453,\nT440 -> T454,\nX285 -> .(T453, T454),\nT415 -> .(T453, T454)"
            },
            {
                "from": 616,
                "to": 621,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 617,
                "to": 664,
                "label": "EVAL with clause\napp_2(.(X294, X295), X296, .(X294, X297)) :- app_2(X295, X296, X297).\nand substitutionX294 -> T465,\nX295 -> T470,\nT414 -> .(T465, T470),\nT416 -> T472,\nT440 -> T473,\nX296 -> .(T472, T473),\nX297 -> T471,\nT415 -> .(T465, T471),\nT466 -> T470,\nT469 -> T471,\nT467 -> T472,\nT468 -> T473"
            },
            {
                "from": 617,
                "to": 665,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 620,
                "to": 627,
                "label": "SUCCESS"
            },
            {
                "from": 664,
                "to": 603,
                "label": "INSTANCE with matching:\nT414 -> T470\nT416 -> T472\nT440 -> T473\nT415 -> T471"
            }
        ],
        "type": "Graph"
    }
}

----------------------------------------

(2)
Obligation:
Rules:
f617_out -> f615_out :|: TRUE
f616_out -> f615_out :|: TRUE
f615_in -> f617_in :|: TRUE
f615_in -> f616_in :|: TRUE
f664_out -> f617_out :|: TRUE
f617_in -> f664_in :|: TRUE
f665_out -> f617_out :|: TRUE
f617_in -> f665_in :|: TRUE
f615_out -> f603_out :|: TRUE
f603_in -> f615_in :|: TRUE
f664_in -> f603_in :|: TRUE
f603_out -> f664_out :|: TRUE
f1_in -> f2_in :|: TRUE
f2_out -> f1_out :|: TRUE
f2_in -> f7_in :|: TRUE
f7_out -> f2_out :|: TRUE
f347_out -> f7_out :|: TRUE
f7_in -> f347_in :|: TRUE
f371_out -> f347_out :|: TRUE
f347_in -> f371_in :|: TRUE
f372_out -> f371_out :|: TRUE
f371_in -> f372_in :|: TRUE
f372_in -> f378_in :|: TRUE
f378_out -> f372_out :|: TRUE
f382_out -> f383_in :|: TRUE
f383_out -> f378_out :|: TRUE
f378_in -> f382_in :|: TRUE
f415_out -> f383_out :|: TRUE
f383_in -> f415_in :|: TRUE
f415_in -> f416_in :|: TRUE
f416_out -> f415_out :|: TRUE
f415_in -> f417_in :|: TRUE
f417_out -> f415_out :|: TRUE
f418_out -> f416_out :|: TRUE
f416_in -> f418_in :|: TRUE
f418_in -> f419_in :|: TRUE
f419_out -> f418_out :|: TRUE
f420_out -> f418_out :|: TRUE
f418_in -> f420_in :|: TRUE
f424_out -> f420_out :|: TRUE
f425_out -> f420_out :|: TRUE
f420_in -> f424_in :|: TRUE
f420_in -> f425_in :|: TRUE
f424_in -> f426_in :|: TRUE
f426_out -> f424_out :|: TRUE
f426_in -> f428_in :|: TRUE
f426_in -> f427_in :|: TRUE
f427_out -> f426_out :|: TRUE
f428_out -> f426_out :|: TRUE
f428_in -> f433_in :|: TRUE
f432_out -> f428_out :|: TRUE
f428_in -> f432_in :|: TRUE
f433_out -> f428_out :|: TRUE
f432_in -> f475_in :|: TRUE
f475_out -> f432_out :|: TRUE
f476_out -> f475_out :|: TRUE
f477_out -> f475_out :|: TRUE
f475_in -> f477_in :|: TRUE
f475_in -> f476_in :|: TRUE
f481_out -> f477_out :|: TRUE
f477_in -> f481_in :|: TRUE
f482_out -> f477_out :|: TRUE
f477_in -> f482_in :|: TRUE
f481_in -> f483_in :|: TRUE
f483_out -> f481_out :|: TRUE
f483_in -> f485_in :|: TRUE
f485_out -> f483_out :|: TRUE
f483_in -> f484_in :|: TRUE
f484_out -> f483_out :|: TRUE
f485_in -> f490_in :|: TRUE
f490_out -> f485_out :|: TRUE
f489_out -> f485_out :|: TRUE
f485_in -> f489_in :|: TRUE
f491_out -> f489_out :|: TRUE
f489_in -> f491_in :|: TRUE
f491_in -> f493_in :|: TRUE
f491_in -> f492_in :|: TRUE
f492_out -> f491_out :|: TRUE
f493_out -> f491_out :|: TRUE
f497_out -> f493_out :|: TRUE
f493_in -> f498_in :|: TRUE
f498_out -> f493_out :|: TRUE
f493_in -> f497_in :|: TRUE
f499_out -> f497_out :|: TRUE
f497_in -> f499_in :|: TRUE
f528_out -> f499_out :|: TRUE
f499_in -> f529_in :|: TRUE
f499_in -> f528_in :|: TRUE
f529_out -> f499_out :|: TRUE
f529_in -> f547_in :|: TRUE
f547_out -> f529_out :|: TRUE
f529_in -> f548_in :|: TRUE
f548_out -> f529_out :|: TRUE
f547_in -> f562_in :|: TRUE
f562_out -> f547_out :|: TRUE
f566_out -> f562_out :|: TRUE
f567_out -> f562_out :|: TRUE
f562_in -> f567_in :|: TRUE
f562_in -> f566_in :|: TRUE
f575_out -> f567_out :|: TRUE
f574_out -> f567_out :|: TRUE
f567_in -> f575_in :|: TRUE
f567_in -> f574_in :|: TRUE
f581_out -> f574_out :|: TRUE
f574_in -> f581_in :|: TRUE
f581_in -> f586_in :|: TRUE
f585_out -> f581_out :|: TRUE
f586_out -> f581_out :|: TRUE
f581_in -> f585_in :|: TRUE
f586_in -> f601_in :|: TRUE
f586_in -> f602_in :|: TRUE
f601_out -> f586_out :|: TRUE
f602_out -> f586_out :|: TRUE
f603_out -> f601_out :|: TRUE
f601_in -> f603_in :|: TRUE
Start term: f1_in

----------------------------------------

(3) IRSwTSimpleDependencyGraphProof (EQUIVALENT)
Constructed simple dependency graph.

Simplified to the following IRSwTs:


----------------------------------------

(4)
TRUE
