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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

fac(a,a)

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

(0) Prolog
(1) PrologToIRSwTTransformerProof [SOUND, 32 ms]
(2) TRUE


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

(0)
Obligation:
Clauses:

fac(X, Y) :- ','(=:=(X, 1), ','(!, =:=(Y, 1))).
fac(X, Y) :- ','(>(X, 1), ','(!, ','(fac(-(X, 1), Z), is(Y, *(Z, X))))).


Query: fac(a,a)
----------------------------------------

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

{
    "root": 2,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(fac X Y)",
                "(',' (=:= X (1)) (',' (!) (=:= Y (1))))"
            ],
            [
                "(fac X Y)",
                "(',' (> X (1)) (',' (!) (',' (fac (- X (1)) Z) (is Y (* Z X)))))"
            ]
        ]
    },
    "graph": {
        "nodes": {
            "1330": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [
                            {
                                "lhs": {
                                    "name": "T11",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "1"
                                },
                                "operation": "="
                            },
                            {
                                "lhs": {
                                    "name": "T12",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "1"
                                },
                                "operation": "="
                            }
                        ]
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": [
                        "T12",
                        "T11"
                    ]
                }
            },
            "type": "Nodes",
            "230": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "1327": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [
                            {
                                "lhs": {
                                    "name": "T11",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "1"
                                },
                                "operation": "="
                            },
                            {
                                "lhs": {
                                    "name": "T12",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "1"
                                },
                                "operation": "="
                            }
                        ]
                    },
                    "ground": ["T12"],
                    "free": [],
                    "exprvars": [
                        "T12",
                        "T11"
                    ]
                }
            },
            "2": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(fac T1 T2)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "1345": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "6": {
                "goal": [
                    {
                        "clause": 0,
                        "scope": 1,
                        "term": "(fac T1 T2)"
                    },
                    {
                        "clause": 1,
                        "scope": 1,
                        "term": "(fac T1 T2)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "226": {
                "goal": [
                    {
                        "clause": -1,
                        "scope": -1,
                        "term": "(',' (!_1) (=:= T12 (1)))"
                    },
                    {
                        "clause": 1,
                        "scope": 1,
                        "term": "(fac T1 T2)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [{
                            "lhs": {
                                "name": "T11",
                                "type": "PlainIntegerVariable"
                            },
                            "type": "PlainIntegerRelation",
                            "rhs": {
                                "type": "PlainIntegerConstant",
                                "value": "1"
                            },
                            "operation": "="
                        }]
                    },
                    "ground": ["T11"],
                    "free": [],
                    "exprvars": ["T11"]
                }
            },
            "1343": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(',' (> T21 (1)) (',' (!_1) (',' (fac (- T21 (1)) X14) (is T22 (* X14 T21)))))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [
                            {
                                "lhs": {
                                    "name": "T11",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "1"
                                },
                                "operation": "!="
                            },
                            {
                                "lhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "1"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "1"
                                },
                                "operation": "!="
                            }
                        ]
                    },
                    "ground": [],
                    "free": ["X14"],
                    "exprvars": ["T11"]
                }
            },
            "7": {
                "goal": [
                    {
                        "clause": -1,
                        "scope": -1,
                        "term": "(',' (=:= T11 (1)) (',' (!_1) (=:= T12 (1))))"
                    },
                    {
                        "clause": 1,
                        "scope": 1,
                        "term": "(fac T1 T2)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "227": {
                "goal": [{
                    "clause": 1,
                    "scope": 1,
                    "term": "(fac T1 T2)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [{
                            "lhs": {
                                "name": "T11",
                                "type": "PlainIntegerVariable"
                            },
                            "type": "PlainIntegerRelation",
                            "rhs": {
                                "type": "PlainIntegerConstant",
                                "value": "1"
                            },
                            "operation": "!="
                        }]
                    },
                    "ground": ["T11"],
                    "free": [],
                    "exprvars": ["T11"]
                }
            },
            "228": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(=:= T12 (1))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [{
                            "lhs": {
                                "name": "T11",
                                "type": "PlainIntegerVariable"
                            },
                            "type": "PlainIntegerRelation",
                            "rhs": {
                                "type": "PlainIntegerConstant",
                                "value": "1"
                            },
                            "operation": "="
                        }]
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": ["T11"]
                }
            },
            "9": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "1329": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [
                            {
                                "lhs": {
                                    "name": "T11",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "1"
                                },
                                "operation": "="
                            },
                            {
                                "lhs": {
                                    "name": "T12",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "1"
                                },
                                "operation": "!="
                            }
                        ]
                    },
                    "ground": ["T12"],
                    "free": [],
                    "exprvars": [
                        "T12",
                        "T11"
                    ]
                }
            }
        },
        "edges": [
            {
                "from": 2,
                "to": 6,
                "label": "CASE"
            },
            {
                "from": 6,
                "to": 7,
                "label": "ONLY EVAL with clause\nfac(X5, X6) :- ','(=:=(X5, 1), ','(!_1, =:=(X6, 1))).\nand substitutionT1 -> T11,\nX5 -> T11,\nT2 -> T12,\nX6 -> T12,\nT9 -> T11,\nT10 -> T12"
            },
            {
                "from": 7,
                "to": 9,
                "label": "IS ERROR"
            },
            {
                "from": 7,
                "to": 226,
                "label": "ARITHCOMP SUCCESS"
            },
            {
                "from": 7,
                "to": 227,
                "label": "ARITHCOMP FAIL"
            },
            {
                "from": 226,
                "to": 228,
                "label": "CUT"
            },
            {
                "from": 227,
                "to": 1343,
                "label": "ONLY EVAL with clause\nfac(X12, X13) :- ','(>(X12, 1), ','(!_1, ','(fac(-(X12, 1), X14), is(X13, *(X14, X12))))).\nand substitutionT1 -> T21,\nX12 -> T21,\nT2 -> T22,\nX13 -> T22,\nT19 -> T21,\nT20 -> T22"
            },
            {
                "from": 228,
                "to": 230,
                "label": "IS ERROR"
            },
            {
                "from": 228,
                "to": 1327,
                "label": "ARITHCOMP SUCCESS"
            },
            {
                "from": 228,
                "to": 1329,
                "label": "ARITHCOMP FAIL"
            },
            {
                "from": 1327,
                "to": 1330,
                "label": "SUCCESS"
            },
            {
                "from": 1343,
                "to": 1345,
                "label": "IS ERROR"
            }
        ],
        "type": "Graph"
    }
}

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

(2)
TRUE