/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) PrologToIRSwTTransformerProof [SOUND, 0 ms]
(2) TRUE


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

(0)
Obligation:
Clauses:

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


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

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

{
    "root": 4,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(p X X (a))",
                "(!)"
            ],
            [
                "(p X Y Z)",
                "(',' (eq Z (a)) (',' (eq X Y) (p X Y Z)))"
            ],
            [
                "(eq X X)",
                null
            ]
        ]
    },
    "graph": {
        "nodes": {
            "22": {
                "goal": [{
                    "clause": 2,
                    "scope": 2,
                    "term": "(',' (eq T20 (a)) (',' (eq T21 T22) (p T21 T22 T20)))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "55": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "23": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(',' (eq T27 T28) (p T27 T28 (a)))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "56": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "24": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "25": {
                "goal": [{
                    "clause": 2,
                    "scope": 3,
                    "term": "(',' (eq T27 T28) (p T27 T28 (a)))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "26": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(p T33 T33 (a))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "27": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "17": {
                "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": []
                }
            },
            "18": {
                "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": []
                }
            },
            "19": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "type": "Nodes",
            "4": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(p T1 T2 T3)"
                }],
                "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": []
                }
            },
            "20": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "53": {
                "goal": [
                    {
                        "clause": 0,
                        "scope": 4,
                        "term": "(p T33 T33 (a))"
                    },
                    {
                        "clause": 1,
                        "scope": 4,
                        "term": "(p T33 T33 (a))"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "21": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(',' (eq T20 (a)) (',' (eq T21 T22) (p T21 T22 T20)))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "54": {
                "goal": [
                    {
                        "clause": -1,
                        "scope": -1,
                        "term": "(!_4)"
                    },
                    {
                        "clause": 1,
                        "scope": 4,
                        "term": "(p T33 T33 (a))"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            }
        },
        "edges": [
            {
                "from": 4,
                "to": 6,
                "label": "CASE"
            },
            {
                "from": 6,
                "to": 17,
                "label": "EVAL with clause\np(X3, X3, a) :- !_1.\nand substitutionT1 -> T6,\nX3 -> T6,\nT2 -> T6,\nT3 -> a"
            },
            {
                "from": 6,
                "to": 18,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 17,
                "to": 19,
                "label": "CUT"
            },
            {
                "from": 18,
                "to": 21,
                "label": "ONLY EVAL with clause\np(X11, X12, X13) :- ','(eq(X13, a), ','(eq(X11, X12), p(X11, X12, X13))).\nand substitutionT1 -> T21,\nX11 -> T21,\nT2 -> T22,\nX12 -> T22,\nT3 -> T20,\nX13 -> T20,\nT19 -> T20,\nT17 -> T21,\nT18 -> T22"
            },
            {
                "from": 19,
                "to": 20,
                "label": "SUCCESS"
            },
            {
                "from": 21,
                "to": 22,
                "label": "CASE"
            },
            {
                "from": 22,
                "to": 23,
                "label": "EVAL with clause\neq(X17, X17).\nand substitutionT20 -> a,\nX17 -> a,\nT26 -> a,\nT21 -> T27,\nT22 -> T28"
            },
            {
                "from": 22,
                "to": 24,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 23,
                "to": 25,
                "label": "CASE"
            },
            {
                "from": 25,
                "to": 26,
                "label": "EVAL with clause\neq(X21, X21).\nand substitutionT27 -> T33,\nX21 -> T33,\nT28 -> T33,\nT32 -> T33"
            },
            {
                "from": 25,
                "to": 27,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 26,
                "to": 53,
                "label": "CASE"
            },
            {
                "from": 53,
                "to": 54,
                "label": "ONLY EVAL with clause\np(X25, X25, a) :- !_4.\nand substitutionT33 -> T37,\nX25 -> T37"
            },
            {
                "from": 54,
                "to": 55,
                "label": "CUT"
            },
            {
                "from": 55,
                "to": 56,
                "label": "SUCCESS"
            }
        ],
        "type": "Graph"
    }
}

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

(2)
TRUE