/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

p(a,a,a)

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

(0) Prolog
(1) PrologToIRSwTTransformerProof [SOUND, 0 ms]
(2) TRUE


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

(0)
Obligation:
Clauses:

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


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

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

{
    "root": 1,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(p X X (a))",
                "(!)"
            ],
            [
                "(p X Y Z)",
                "(',' (= Z (a)) (',' (= X Y) (p X Y Z)))"
            ]
        ]
    },
    "graph": {
        "nodes": {
            "16": {
                "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": []
                }
            },
            "17": {
                "goal": [{
                    "clause": 1,
                    "scope": 1,
                    "term": "(p T1 T2 T3)"
                }],
                "kb": {
                    "nonunifying": [[
                        "(p T1 T2 T3)",
                        "(p X3 X3 (a))"
                    ]],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": ["X3"],
                    "exprvars": []
                }
            },
            "18": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "180": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "type": "Nodes",
            "131": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(p T26 T26 (a))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "132": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "1": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(p T1 T2 T3)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "178": {
                "goal": [
                    {
                        "clause": -1,
                        "scope": -1,
                        "term": "(!_2)"
                    },
                    {
                        "clause": 1,
                        "scope": 2,
                        "term": "(p T26 T26 (a))"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "3": {
                "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": []
                }
            },
            "179": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "126": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(',' (= T19 (a)) (',' (= T20 T21) (p T20 T21 T19)))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "127": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(',' (= T22 T23) (p T22 T23 (a)))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "138": {
                "goal": [
                    {
                        "clause": 0,
                        "scope": 2,
                        "term": "(p T26 T26 (a))"
                    },
                    {
                        "clause": 1,
                        "scope": 2,
                        "term": "(p T26 T26 (a))"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "128": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "118": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            }
        },
        "edges": [
            {
                "from": 1,
                "to": 3,
                "label": "CASE"
            },
            {
                "from": 3,
                "to": 16,
                "label": "EVAL with clause\np(X3, X3, a) :- !_1.\nand substitutionT1 -> T6,\nX3 -> T6,\nT2 -> T6,\nT3 -> a"
            },
            {
                "from": 3,
                "to": 17,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 16,
                "to": 18,
                "label": "CUT"
            },
            {
                "from": 17,
                "to": 126,
                "label": "ONLY EVAL with clause\np(X10, X11, X12) :- ','(=(X12, a), ','(=(X10, X11), p(X10, X11, X12))).\nand substitutionT1 -> T20,\nX10 -> T20,\nT2 -> T21,\nX11 -> T21,\nT3 -> T19,\nX12 -> T19,\nT18 -> T19,\nT16 -> T20,\nT17 -> T21"
            },
            {
                "from": 18,
                "to": 118,
                "label": "SUCCESS"
            },
            {
                "from": 126,
                "to": 127,
                "label": "UNIFY CASE with substitutionT19 -> a,\nT20 -> T22,\nT21 -> T23"
            },
            {
                "from": 126,
                "to": 128,
                "label": "UNIFY-BACKTRACK"
            },
            {
                "from": 127,
                "to": 131,
                "label": "UNIFY CASE with substitutionT22 -> T26,\nT23 -> T26,\nT25 -> T26"
            },
            {
                "from": 127,
                "to": 132,
                "label": "UNIFY-BACKTRACK"
            },
            {
                "from": 131,
                "to": 138,
                "label": "CASE"
            },
            {
                "from": 138,
                "to": 178,
                "label": "ONLY EVAL with clause\np(X16, X16, a) :- !_2.\nand substitutionT26 -> T30,\nX16 -> T30"
            },
            {
                "from": 178,
                "to": 179,
                "label": "CUT"
            },
            {
                "from": 179,
                "to": 180,
                "label": "SUCCESS"
            }
        ],
        "type": "Graph"
    }
}

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

(2)
TRUE