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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

test_fun(g,g,g)

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

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


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

(0)
Obligation:
Clauses:

test_fun(X, Y, Z) :- ','(=<(Y, 0), !).
test_fun(X, Y, Z) :- loop(X, Y, Z).
loop(X, Y, Z) :- <(X, Z).
loop(X, Y, Z) :- ','(>=(X, Z), loop_body(X, Y, Z)).
loop_body(X, Y, Z) :- =<(Y, 0).
loop_body(X, Y, Z) :- ','(>(Y, 0), ','(is(Z1, +(Z, Y)), loop(X, Y, Z1))).


Query: test_fun(g,g,g)
----------------------------------------

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

{
    "root": 2,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(test_fun X Y Z)",
                "(',' (=< Y (0)) (!))"
            ],
            [
                "(test_fun X Y Z)",
                "(loop X Y Z)"
            ],
            [
                "(loop X Y Z)",
                "(< X Z)"
            ],
            [
                "(loop X Y Z)",
                "(',' (>= X Z) (loop_body X Y Z))"
            ],
            [
                "(loop_body X Y Z)",
                "(=< Y (0))"
            ],
            [
                "(loop_body X Y Z)",
                "(',' (> Y (0)) (',' (is Z1 (+ Z Y)) (loop X Y Z1)))"
            ]
        ]
    },
    "graph": {
        "nodes": {
            "11": {
                "goal": [
                    {
                        "clause": -1,
                        "scope": -1,
                        "term": "(',' (=< T11 (0)) (!_1))"
                    },
                    {
                        "clause": 1,
                        "scope": 1,
                        "term": "(test_fun T10 T11 T12)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [
                        "T10",
                        "T11",
                        "T12"
                    ],
                    "free": [],
                    "exprvars": []
                }
            },
            "12": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "type": "Nodes",
            "2": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(test_fun T1 T2 T3)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [
                        "T1",
                        "T2",
                        "T3"
                    ],
                    "free": [],
                    "exprvars": []
                }
            },
            "520": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(< T40 T42)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [
                            {
                                "lhs": {
                                    "name": "T11",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": ">"
                            },
                            {
                                "lhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": ">"
                            },
                            {
                                "lhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": ">"
                            },
                            {
                                "lhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": ">"
                            }
                        ]
                    },
                    "ground": [
                        "T40",
                        "T42"
                    ],
                    "free": [],
                    "exprvars": [
                        "T41",
                        "T23",
                        "T11"
                    ]
                }
            },
            "4": {
                "goal": [
                    {
                        "clause": 0,
                        "scope": 1,
                        "term": "(test_fun T1 T2 T3)"
                    },
                    {
                        "clause": 1,
                        "scope": 1,
                        "term": "(test_fun T1 T2 T3)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [
                        "T1",
                        "T2",
                        "T3"
                    ],
                    "free": [],
                    "exprvars": []
                }
            },
            "521": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "512": {
                "goal": [{
                    "clause": 2,
                    "scope": 2,
                    "term": "(loop T22 T23 T24)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [
                            {
                                "lhs": {
                                    "name": "T11",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": ">"
                            },
                            {
                                "lhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": ">"
                            }
                        ]
                    },
                    "ground": [
                        "T22",
                        "T23",
                        "T24"
                    ],
                    "free": [],
                    "exprvars": [
                        "T23",
                        "T11"
                    ]
                }
            },
            "502": {
                "goal": [
                    {
                        "clause": -1,
                        "scope": -1,
                        "term": "(!_1)"
                    },
                    {
                        "clause": 1,
                        "scope": 1,
                        "term": "(test_fun T10 T11 T12)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [{
                            "lhs": {
                                "name": "T11",
                                "type": "PlainIntegerVariable"
                            },
                            "type": "PlainIntegerRelation",
                            "rhs": {
                                "type": "PlainIntegerConstant",
                                "value": "0"
                            },
                            "operation": "<="
                        }]
                    },
                    "ground": [
                        "T12",
                        "T11",
                        "T10"
                    ],
                    "free": [],
                    "exprvars": ["T11"]
                }
            },
            "513": {
                "goal": [{
                    "clause": 3,
                    "scope": 2,
                    "term": "(loop T22 T23 T24)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [
                            {
                                "lhs": {
                                    "name": "T11",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": ">"
                            },
                            {
                                "lhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": ">"
                            }
                        ]
                    },
                    "ground": [
                        "T22",
                        "T23",
                        "T24"
                    ],
                    "free": [],
                    "exprvars": [
                        "T23",
                        "T11"
                    ]
                }
            },
            "503": {
                "goal": [{
                    "clause": 1,
                    "scope": 1,
                    "term": "(test_fun T10 T11 T12)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [{
                            "lhs": {
                                "name": "T11",
                                "type": "PlainIntegerVariable"
                            },
                            "type": "PlainIntegerRelation",
                            "rhs": {
                                "type": "PlainIntegerConstant",
                                "value": "0"
                            },
                            "operation": ">"
                        }]
                    },
                    "ground": [
                        "T12",
                        "T11",
                        "T10"
                    ],
                    "free": [],
                    "exprvars": ["T11"]
                }
            },
            "504": {
                "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": "0"
                            },
                            "operation": "<="
                        }]
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": ["T11"]
                }
            },
            "505": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [{
                            "lhs": {
                                "name": "T11",
                                "type": "PlainIntegerVariable"
                            },
                            "type": "PlainIntegerRelation",
                            "rhs": {
                                "type": "PlainIntegerConstant",
                                "value": "0"
                            },
                            "operation": "<="
                        }]
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": ["T11"]
                }
            },
            "506": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(loop T22 T23 T24)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [
                            {
                                "lhs": {
                                    "name": "T11",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": ">"
                            },
                            {
                                "lhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": ">"
                            }
                        ]
                    },
                    "ground": [
                        "T22",
                        "T23",
                        "T24"
                    ],
                    "free": [],
                    "exprvars": [
                        "T23",
                        "T11"
                    ]
                }
            },
            "508": {
                "goal": [
                    {
                        "clause": 2,
                        "scope": 2,
                        "term": "(loop T22 T23 T24)"
                    },
                    {
                        "clause": 3,
                        "scope": 2,
                        "term": "(loop T22 T23 T24)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [
                            {
                                "lhs": {
                                    "name": "T11",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": ">"
                            },
                            {
                                "lhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": ">"
                            }
                        ]
                    },
                    "ground": [
                        "T22",
                        "T23",
                        "T24"
                    ],
                    "free": [],
                    "exprvars": [
                        "T23",
                        "T11"
                    ]
                }
            },
            "1615": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "1614": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(',' (>= T49 T51) (loop_body T49 T50 T51))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": [
                            {
                                "lhs": {
                                    "name": "T11",
                                    "type": "PlainIntegerVariable"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": ">"
                            },
                            {
                                "lhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": ">"
                            },
                            {
                                "lhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": ">"
                            },
                            {
                                "lhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "type": "PlainIntegerRelation",
                                "rhs": {
                                    "type": "PlainIntegerConstant",
                                    "value": "0"
                                },
                                "operation": ">"
                            }
                        ]
                    },
                    "ground": [
                        "T49",
                        "T50",
                        "T51"
                    ],
                    "free": [],
                    "exprvars": [
                        "T23",
                        "T50",
                        "T11"
                    ]
                }
            }
        },
        "edges": [
            {
                "from": 2,
                "to": 4,
                "label": "CASE"
            },
            {
                "from": 4,
                "to": 11,
                "label": "ONLY EVAL with clause\ntest_fun(X7, X8, X9) :- ','(=<(X8, 0), !_1).\nand substitutionT1 -> T10,\nX7 -> T10,\nT2 -> T11,\nX8 -> T11,\nT3 -> T12,\nX9 -> T12"
            },
            {
                "from": 11,
                "to": 12,
                "label": "IS ERROR"
            },
            {
                "from": 11,
                "to": 502,
                "label": "ARITHCOMP SUCCESS"
            },
            {
                "from": 11,
                "to": 503,
                "label": "ARITHCOMP FAIL"
            },
            {
                "from": 502,
                "to": 504,
                "label": "CUT"
            },
            {
                "from": 503,
                "to": 506,
                "label": "ONLY EVAL with clause\ntest_fun(X19, X20, X21) :- loop(X19, X20, X21).\nand substitutionT10 -> T22,\nX19 -> T22,\nT11 -> T23,\nX20 -> T23,\nT12 -> T24,\nX21 -> T24"
            },
            {
                "from": 504,
                "to": 505,
                "label": "SUCCESS"
            },
            {
                "from": 506,
                "to": 508,
                "label": "CASE"
            },
            {
                "from": 508,
                "to": 512,
                "label": "PARALLEL"
            },
            {
                "from": 508,
                "to": 513,
                "label": "PARALLEL"
            },
            {
                "from": 512,
                "to": 520,
                "label": "ONLY EVAL with clause\nloop(X37, X38, X39) :- <(X37, X39).\nand substitutionT22 -> T40,\nX37 -> T40,\nT23 -> T41,\nX38 -> T41,\nT24 -> T42,\nX39 -> T42"
            },
            {
                "from": 513,
                "to": 1614,
                "label": "ONLY EVAL with clause\nloop(X46, X47, X48) :- ','(>=(X46, X48), loop_body(X46, X47, X48)).\nand substitutionT22 -> T49,\nX46 -> T49,\nT23 -> T50,\nX47 -> T50,\nT24 -> T51,\nX48 -> T51"
            },
            {
                "from": 520,
                "to": 521,
                "label": "IS ERROR"
            },
            {
                "from": 1614,
                "to": 1615,
                "label": "IS ERROR"
            }
        ],
        "type": "Graph"
    }
}

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

(2)
TRUE