/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.pl /export/starexec/sandbox2/output/output_files


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


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.pl
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Left Termination of the query pattern

p(a,a,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:

p(X, X, 1) :- !.
p(X, Y, Z) :- ','(=(Z, 1), ','(=(Y, X), p(X, Y, Z))).
=(X, X).


Query: p(a,a,a)
----------------------------------------

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

(2)
Obligation:
Clauses:

p(X, X, 1) :- !.
p(X, Y, Z) :- ','(user_defined_=(Z, 1), ','(user_defined_=(Y, X), p(X, Y, Z))).
user_defined_=(X, X).


Query: p(a,a,a)
----------------------------------------

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

{
    "root": 2,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(p X X (1))",
                "(!)"
            ],
            [
                "(p X Y Z)",
                "(',' (user_defined_= Z (1)) (',' (user_defined_= Y X) (p X Y Z)))"
            ],
            [
                "(user_defined_= X X)",
                null
            ]
        ]
    },
    "graph": {
        "nodes": {
            "type": "Nodes",
            "130": {
                "goal": [
                    {
                        "clause": -1,
                        "scope": -1,
                        "term": "(!_4)"
                    },
                    {
                        "clause": 1,
                        "scope": 4,
                        "term": "(p T33 T33 (1))"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "131": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "110": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "132": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "122": {
                "goal": [{
                    "clause": 2,
                    "scope": 3,
                    "term": "(',' (user_defined_= T27 T28) (p T28 T27 (1)))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "2": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(p T1 T2 T3)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "123": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(p T33 T33 (1))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "113": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(',' (user_defined_= T20 (1)) (',' (user_defined_= T21 T22) (p T22 T21 T20)))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "124": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "103": {
                "goal": [{
                    "clause": 1,
                    "scope": 1,
                    "term": "(p T1 T2 T3)"
                }],
                "kb": {
                    "nonunifying": [[
                        "(p T1 T2 T3)",
                        "(p X3 X3 (1))"
                    ]],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": ["X3"],
                    "exprvars": []
                }
            },
            "125": {
                "goal": [
                    {
                        "clause": 0,
                        "scope": 4,
                        "term": "(p T33 T33 (1))"
                    },
                    {
                        "clause": 1,
                        "scope": 4,
                        "term": "(p T33 T33 (1))"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "6": {
                "goal": [
                    {
                        "clause": 0,
                        "scope": 1,
                        "term": "(p T1 T2 T3)"
                    },
                    {
                        "clause": 1,
                        "scope": 1,
                        "term": "(p T1 T2 T3)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "116": {
                "goal": [{
                    "clause": 2,
                    "scope": 2,
                    "term": "(',' (user_defined_= T20 (1)) (',' (user_defined_= T21 T22) (p T22 T21 T20)))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "107": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "118": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(',' (user_defined_= T27 T28) (p T28 T27 (1)))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "119": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "87": {
                "goal": [
                    {
                        "clause": -1,
                        "scope": -1,
                        "term": "(!_1)"
                    },
                    {
                        "clause": 1,
                        "scope": 1,
                        "term": "(p T1 T2 T3)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            }
        },
        "edges": [
            {
                "from": 2,
                "to": 6,
                "label": "CASE"
            },
            {
                "from": 6,
                "to": 87,
                "label": "EVAL with clause\np(X3, X3, 1) :- !_1.\nand substitutionT1 -> T6,\nX3 -> T6,\nT2 -> T6,\nT3 -> 1"
            },
            {
                "from": 6,
                "to": 103,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 87,
                "to": 107,
                "label": "CUT"
            },
            {
                "from": 103,
                "to": 113,
                "label": "ONLY EVAL with clause\np(X11, X12, X13) :- ','(user_defined_=(X13, 1), ','(user_defined_=(X12, X11), p(X11, X12, X13))).\nand substitutionT1 -> T22,\nX11 -> T22,\nT2 -> T21,\nX12 -> T21,\nT3 -> T20,\nX13 -> T20,\nT19 -> T20,\nT18 -> T21,\nT17 -> T22"
            },
            {
                "from": 107,
                "to": 110,
                "label": "SUCCESS"
            },
            {
                "from": 113,
                "to": 116,
                "label": "CASE"
            },
            {
                "from": 116,
                "to": 118,
                "label": "EVAL with clause\nuser_defined_=(X17, X17).\nand substitutionT20 -> 1,\nX17 -> 1,\nT26 -> 1,\nT21 -> T27,\nT22 -> T28"
            },
            {
                "from": 116,
                "to": 119,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 118,
                "to": 122,
                "label": "CASE"
            },
            {
                "from": 122,
                "to": 123,
                "label": "EVAL with clause\nuser_defined_=(X21, X21).\nand substitutionT27 -> T33,\nX21 -> T33,\nT28 -> T33,\nT32 -> T33"
            },
            {
                "from": 122,
                "to": 124,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 123,
                "to": 125,
                "label": "CASE"
            },
            {
                "from": 125,
                "to": 130,
                "label": "ONLY EVAL with clause\np(X25, X25, 1) :- !_4.\nand substitutionT33 -> T37,\nX25 -> T37"
            },
            {
                "from": 130,
                "to": 131,
                "label": "CUT"
            },
            {
                "from": 131,
                "to": 132,
                "label": "SUCCESS"
            }
        ],
        "type": "Graph"
    }
}

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

(4)
TRUE