/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.pl /export/starexec/sandbox/output/output_files


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


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.pl
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Left Termination of the query pattern

minus(g,g,a)

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

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


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

(0)
Obligation:
Clauses:

minus(X, Y, Z) :- ','(f(X, 0), ','(!, =(Z, 0))).
f(X, Y) :- ','(!, =(X, Y)).
f(X, Y) :- f(X, Y).
=(X, X).


Query: minus(g,g,a)
----------------------------------------

(1) BuiltinConflictTransformerProof (EQUIVALENT)
Renamed defined predicates conflicting with built-in predicates [PROLOG].
----------------------------------------

(2)
Obligation:
Clauses:

minus(X, Y, Z) :- ','(f(X, 0), ','(!, user_defined_=(Z, 0))).
f(X, Y) :- ','(!, user_defined_=(X, Y)).
f(X, Y) :- f(X, Y).
user_defined_=(X, X).


Query: minus(g,g,a)
----------------------------------------

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

{
    "root": 14,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(minus X Y Z)",
                "(',' (f X (0)) (',' (!) (user_defined_= Z (0))))"
            ],
            [
                "(f X Y)",
                "(',' (!) (user_defined_= X Y))"
            ],
            [
                "(f X Y)",
                "(f X Y)"
            ],
            [
                "(user_defined_= X X)",
                null
            ]
        ]
    },
    "graph": {
        "nodes": {
            "14": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(minus T1 T2 T3)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [
                        "T1",
                        "T2"
                    ],
                    "free": [],
                    "exprvars": []
                }
            },
            "15": {
                "goal": [{
                    "clause": 0,
                    "scope": 1,
                    "term": "(minus T1 T2 T3)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [
                        "T1",
                        "T2"
                    ],
                    "free": [],
                    "exprvars": []
                }
            },
            "191": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(user_defined_= T15 (0))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "192": {
                "goal": [{
                    "clause": 3,
                    "scope": 4,
                    "term": "(user_defined_= T15 (0))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "193": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "type": "Nodes",
            "194": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "195": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "110": {
                "goal": [{
                    "clause": 3,
                    "scope": 3,
                    "term": "(user_defined_= T20 (0))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T20"],
                    "free": [],
                    "exprvars": []
                }
            },
            "100": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(',' (f T12 (0)) (',' (!_1) (user_defined_= T15 (0))))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T12"],
                    "free": [],
                    "exprvars": []
                }
            },
            "111": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "124": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "105": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(f T12 (0))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T12"],
                    "free": [],
                    "exprvars": []
                }
            },
            "106": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(',' (!_1) (user_defined_= T15 (0)))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "107": {
                "goal": [
                    {
                        "clause": 1,
                        "scope": 2,
                        "term": "(f T12 (0))"
                    },
                    {
                        "clause": 2,
                        "scope": 2,
                        "term": "(f T12 (0))"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T12"],
                    "free": [],
                    "exprvars": []
                }
            },
            "118": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "108": {
                "goal": [
                    {
                        "clause": -1,
                        "scope": -1,
                        "term": "(',' (!_2) (user_defined_= T20 (0)))"
                    },
                    {
                        "clause": 2,
                        "scope": 2,
                        "term": "(f T20 (0))"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T20"],
                    "free": [],
                    "exprvars": []
                }
            },
            "109": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(user_defined_= T20 (0))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T20"],
                    "free": [],
                    "exprvars": []
                }
            }
        },
        "edges": [
            {
                "from": 14,
                "to": 15,
                "label": "CASE"
            },
            {
                "from": 15,
                "to": 100,
                "label": "ONLY EVAL with clause\nminus(X9, X10, X11) :- ','(f(X9, 0), ','(!_1, user_defined_=(X11, 0))).\nand substitutionT1 -> T12,\nX9 -> T12,\nT2 -> T13,\nX10 -> T13,\nT3 -> T15,\nX11 -> T15,\nT14 -> T15"
            },
            {
                "from": 100,
                "to": 105,
                "label": "SPLIT 1"
            },
            {
                "from": 100,
                "to": 106,
                "label": "SPLIT 2\nnew knowledge:\nT12 is ground"
            },
            {
                "from": 105,
                "to": 107,
                "label": "CASE"
            },
            {
                "from": 106,
                "to": 191,
                "label": "CUT"
            },
            {
                "from": 107,
                "to": 108,
                "label": "ONLY EVAL with clause\nf(X20, X21) :- ','(!_2, user_defined_=(X20, X21)).\nand substitutionT12 -> T20,\nX20 -> T20,\nX21 -> 0"
            },
            {
                "from": 108,
                "to": 109,
                "label": "CUT"
            },
            {
                "from": 109,
                "to": 110,
                "label": "CASE"
            },
            {
                "from": 110,
                "to": 111,
                "label": "EVAL with clause\nuser_defined_=(X24, X24).\nand substitutionT20 -> 0,\nX24 -> 0,\nT23 -> 0"
            },
            {
                "from": 110,
                "to": 118,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 111,
                "to": 124,
                "label": "SUCCESS"
            },
            {
                "from": 191,
                "to": 192,
                "label": "CASE"
            },
            {
                "from": 192,
                "to": 193,
                "label": "EVAL with clause\nuser_defined_=(X27, X27).\nand substitutionT15 -> 0,\nX27 -> 0,\nT26 -> 0"
            },
            {
                "from": 192,
                "to": 194,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 193,
                "to": 195,
                "label": "SUCCESS"
            }
        ],
        "type": "Graph"
    }
}

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

(4)
TRUE