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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

main(g,g)

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

(0) Prolog
(1) PrologToIRSwTTransformerProof [SOUND, 28 ms]
(2) TRUE


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

(0)
Obligation:
Clauses:

main(M, N) :- ','(>(M, 0), ','(>(N, 0), gcd(M, N))).
gcd(Y1, Y2) :- ','(=<(Y1, 0), !).
gcd(Y1, Y2) :- ','(=<(Y2, 0), !).
gcd(Y1, Y2) :- ','(=:=(Y2, 0), !).
gcd(Y1, Y2) :- ','(>(Y1, Y2), ','(gcd(-(Y1, Y2), Y2), !)).
gcd(Y1, Y2) :- gcd(Y1, -(Y2, Y1)).


Query: main(g,g)
----------------------------------------

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

{
    "root": 1,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(main M N)",
                "(',' (> M (0)) (',' (> N (0)) (gcd M N)))"
            ],
            [
                "(gcd Y1 Y2)",
                "(',' (=< Y1 (0)) (!))"
            ],
            [
                "(gcd Y1 Y2)",
                "(',' (=< Y2 (0)) (!))"
            ],
            [
                "(gcd Y1 Y2)",
                "(',' (=:= Y2 (0)) (!))"
            ],
            [
                "(gcd Y1 Y2)",
                "(',' (> Y1 Y2) (',' (gcd (- Y1 Y2) Y2) (!)))"
            ],
            [
                "(gcd Y1 Y2)",
                "(gcd Y1 (- Y2 Y1))"
            ]
        ]
    },
    "graph": {
        "nodes": {
            "12": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "type": "Nodes",
            "1998": {
                "goal": [
                    {
                        "clause": -1,
                        "scope": -1,
                        "term": "(',' (=< T22 (0)) (!_2))"
                    },
                    {
                        "clause": 3,
                        "scope": 2,
                        "term": "(gcd T21 T22)"
                    },
                    {
                        "clause": 4,
                        "scope": 2,
                        "term": "(gcd T21 T22)"
                    },
                    {
                        "clause": 5,
                        "scope": 2,
                        "term": "(gcd T21 T22)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [
                            {
                                "lhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "name": "T7",
                                    "type": "PlainIntegerVariable"
                                },
                                "operation": "<"
                            },
                            {
                                "lhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "name": "T8",
                                    "type": "PlainIntegerVariable"
                                },
                                "operation": "<"
                            },
                            {
                                "lhs": {
                                    "name": "T15",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "name": "T7",
                                    "type": "PlainIntegerVariable"
                                },
                                "operation": "<"
                            },
                            {
                                "lhs": {
                                    "name": "T16",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "name": "T8",
                                    "type": "PlainIntegerVariable"
                                },
                                "operation": "<"
                            },
                            {
                                "lhs": {
                                    "name": "T15",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": ">"
                            },
                            {
                                "lhs": {
                                    "name": "T7",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
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                                    "type": "PlainIntegerVariable"
                                },
                                "operation": "<"
                            },
                            {
                                "lhs": {
                                    "name": "T8",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "name": "T8",
                                    "type": "PlainIntegerVariable"
                                },
                                "operation": "<"
                            },
                            {
                                "lhs": {
                                    "name": "T7",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "name": "T7",
                                    "type": "PlainIntegerVariable"
                                },
                                "operation": "<"
                            },
                            {
                                "lhs": {
                                    "name": "T8",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "name": "T8",
                                    "type": "PlainIntegerVariable"
                                },
                                "operation": "<"
                            },
                            {
                                "lhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": ">"
                            }
                        ]
                    },
                    "ground": [
                        "T21",
                        "T22"
                    ],
                    "free": [],
                    "exprvars": [
                        "T7",
                        "T22",
                        "T8",
                        "T16",
                        "T21",
                        "T15"
                    ]
                }
            },
            "1": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(main T1 T2)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [
                        "T1",
                        "T2"
                    ],
                    "free": [],
                    "exprvars": []
                }
            },
            "1975": {
                "goal": [
                    {
                        "clause": -1,
                        "scope": -1,
                        "term": "(',' (=< T15 (0)) (!_2))"
                    },
                    {
                        "clause": 2,
                        "scope": 2,
                        "term": "(gcd T15 T16)"
                    },
                    {
                        "clause": 3,
                        "scope": 2,
                        "term": "(gcd T15 T16)"
                    },
                    {
                        "clause": 4,
                        "scope": 2,
                        "term": "(gcd T15 T16)"
                    },
                    {
                        "clause": 5,
                        "scope": 2,
                        "term": "(gcd T15 T16)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [
                            {
                                "lhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "name": "T7",
                                    "type": "PlainIntegerVariable"
                                },
                                "operation": "<"
                            },
                            {
                                "lhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "name": "T8",
                                    "type": "PlainIntegerVariable"
                                },
                                "operation": "<"
                            },
                            {
                                "lhs": {
                                    "name": "T15",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "name": "T7",
                                    "type": "PlainIntegerVariable"
                                },
                                "operation": "<"
                            },
                            {
                                "lhs": {
                                    "name": "T16",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "name": "T8",
                                    "type": "PlainIntegerVariable"
                                },
                                "operation": "<"
                            }
                        ]
                    },
                    "ground": [
                        "T15",
                        "T16"
                    ],
                    "free": [],
                    "exprvars": [
                        "T7",
                        "T8",
                        "T16",
                        "T15"
                    ]
                }
            },
            "1997": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [
                            {
                                "lhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "name": "T7",
                                    "type": "PlainIntegerVariable"
                                },
                                "operation": "<"
                            },
                            {
                                "lhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "name": "T8",
                                    "type": "PlainIntegerVariable"
                                },
                                "operation": "<"
                            },
                            {
                                "lhs": {
                                    "name": "T15",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "name": "T7",
                                    "type": "PlainIntegerVariable"
                                },
                                "operation": "<"
                            },
                            {
                                "lhs": {
                                    "name": "T16",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "name": "T8",
                                    "type": "PlainIntegerVariable"
                                },
                                "operation": "<"
                            },
                            {
                                "lhs": {
                                    "name": "T15",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": "<="
                            }
                        ]
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": [
                        "T7",
                        "T8",
                        "T16",
                        "T15"
                    ]
                }
            },
            "1963": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "1974": {
                "goal": [
                    {
                        "clause": 1,
                        "scope": 2,
                        "term": "(gcd T7 T8)"
                    },
                    {
                        "clause": 2,
                        "scope": 2,
                        "term": "(gcd T7 T8)"
                    },
                    {
                        "clause": 3,
                        "scope": 2,
                        "term": "(gcd T7 T8)"
                    },
                    {
                        "clause": 4,
                        "scope": 2,
                        "term": "(gcd T7 T8)"
                    },
                    {
                        "clause": 5,
                        "scope": 2,
                        "term": "(gcd T7 T8)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [
                            {
                                "lhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "name": "T7",
                                    "type": "PlainIntegerVariable"
                                },
                                "operation": "<"
                            },
                            {
                                "lhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "name": "T8",
                                    "type": "PlainIntegerVariable"
                                },
                                "operation": "<"
                            }
                        ]
                    },
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                        "T7",
                        "T8"
                    ],
                    "free": [],
                    "exprvars": [
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                        "T8"
                    ]
                }
            },
            "1962": {
                "goal": [],
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                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [{
                            "lhs": {
                                "type": "PlainIntegerConstant",
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                            },
                            "type": "PlainIntegerRelation",
                            "rhs": {
                                "name": "T7",
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                            },
                            "operation": ">="
                        }]
                    },
                    "ground": [
                        "T7",
                        "T8"
                    ],
                    "free": [],
                    "exprvars": ["T7"]
                }
            },
            "1973": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
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                            {
                                "lhs": {
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                                "type": "PlainIntegerRelation",
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                    },
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                }
            },
            "1995": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
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                            {
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                            },
                            {
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                                "operation": "<"
                            },
                            {
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                                "operation": "<"
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                            {
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                                    "name": "T15",
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                                "type": "PlainIntegerRelation",
                                "rhs": {
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                                    "value": "0"
                                },
                                "operation": "<="
                            }
                        ]
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": [
                        "T7",
                        "T8",
                        "T16",
                        "T15"
                    ]
                }
            },
            "1961": {
                "goal": [{
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                    "scope": -1,
                    "term": "(',' (> T8 (0)) (gcd T7 T8))"
                }],
                "kb": {
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                    "intvars": {},
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                            },
                            "operation": "<"
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                    },
                    "ground": [
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                    ],
                    "free": [],
                    "exprvars": ["T7"]
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            },
            "1972": {
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                            },
                            {
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                        ]
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                    "exprvars": [
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                    ]
                }
            },
            "5": {
                "goal": [{
                    "clause": 0,
                    "scope": 1,
                    "term": "(main T1 T2)"
                }],
                "kb": {
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                    "intvars": {},
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                    },
                    "ground": [
                        "T1",
                        "T2"
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            },
            "1992": {
                "goal": [
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                        "clause": 2,
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                        "term": "(gcd T15 T16)"
                    },
                    {
                        "clause": 4,
                        "scope": 2,
                        "term": "(gcd T15 T16)"
                    },
                    {
                        "clause": 5,
                        "scope": 2,
                        "term": "(gcd T15 T16)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
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                            {
                                "lhs": {
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                            {
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                                    "name": "T7",
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                            {
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                            {
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                                "operation": ">"
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                        ]
                    },
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                        "T7",
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                    ]
                }
            },
            "1991": {
                "goal": [
                    {
                        "clause": -1,
                        "scope": -1,
                        "term": "(!_2)"
                    },
                    {
                        "clause": 2,
                        "scope": 2,
                        "term": "(gcd T15 T16)"
                    },
                    {
                        "clause": 3,
                        "scope": 2,
                        "term": "(gcd T15 T16)"
                    },
                    {
                        "clause": 4,
                        "scope": 2,
                        "term": "(gcd T15 T16)"
                    },
                    {
                        "clause": 5,
                        "scope": 2,
                        "term": "(gcd T15 T16)"
                    }
                ],
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                            {
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                            {
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                            {
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                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "name": "T8",
                                    "type": "PlainIntegerVariable"
                                },
                                "operation": "<"
                            },
                            {
                                "lhs": {
                                    "name": "T15",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": "<="
                            }
                        ]
                    },
                    "ground": [
                        "T16",
                        "T15"
                    ],
                    "free": [],
                    "exprvars": [
                        "T7",
                        "T8",
                        "T16",
                        "T15"
                    ]
                }
            },
            "8": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(',' (> T7 (0)) (',' (> T8 (0)) (gcd T7 T8)))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [
                        "T7",
                        "T8"
                    ],
                    "free": [],
                    "exprvars": []
                }
            }
        },
        "edges": [
            {
                "from": 1,
                "to": 5,
                "label": "CASE"
            },
            {
                "from": 5,
                "to": 8,
                "label": "ONLY EVAL with clause\nmain(X5, X6) :- ','(>(X5, 0), ','(>(X6, 0), gcd(X5, X6))).\nand substitutionT1 -> T7,\nX5 -> T7,\nT2 -> T8,\nX6 -> T8"
            },
            {
                "from": 8,
                "to": 12,
                "label": "IS ERROR"
            },
            {
                "from": 8,
                "to": 1961,
                "label": "ARITHCOMP SUCCESS"
            },
            {
                "from": 8,
                "to": 1962,
                "label": "ARITHCOMP FAIL"
            },
            {
                "from": 1961,
                "to": 1963,
                "label": "IS ERROR"
            },
            {
                "from": 1961,
                "to": 1972,
                "label": "ARITHCOMP SUCCESS"
            },
            {
                "from": 1961,
                "to": 1973,
                "label": "ARITHCOMP FAIL"
            },
            {
                "from": 1972,
                "to": 1974,
                "label": "CASE"
            },
            {
                "from": 1974,
                "to": 1975,
                "label": "ONLY EVAL with clause\ngcd(X13, X14) :- ','(=<(X13, 0), !_2).\nand substitutionT7 -> T15,\nX13 -> T15,\nT8 -> T16,\nX14 -> T16"
            },
            {
                "from": 1975,
                "to": 1991,
                "label": "ARITHCOMP SUCCESS"
            },
            {
                "from": 1975,
                "to": 1992,
                "label": "ARITHCOMP FAIL"
            },
            {
                "from": 1991,
                "to": 1995,
                "label": "CUT"
            },
            {
                "from": 1992,
                "to": 1998,
                "label": "ONLY EVAL with clause\ngcd(X19, X20) :- ','(=<(X20, 0), !_2).\nand substitutionT15 -> T21,\nX19 -> T21,\nT16 -> T22,\nX20 -> T22"
            },
            {
                "from": 1995,
                "to": 1997,
                "label": "SUCCESS"
            }
        ],
        "type": "Graph"
    }
}

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

(2)
TRUE