/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.pl /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.pl
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Left Termination of the query pattern

p(g)

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

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


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

(0)
Obligation:
Clauses:

p(b).
p(a) :- p1(X).
p1(b) :- !.
p1(a) :- p1(X).


Query: p(g)
----------------------------------------

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

{
    "root": 2,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(p (b))",
                null
            ],
            [
                "(p (a))",
                "(p1 X)"
            ],
            [
                "(p1 (b))",
                "(!)"
            ],
            [
                "(p1 (a))",
                "(p1 X)"
            ]
        ]
    },
    "graph": {
        "nodes": {
            "88": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "23": {
                "goal": [{
                    "clause": 0,
                    "scope": 1,
                    "term": "(p T1)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T1"],
                    "free": [],
                    "exprvars": []
                }
            },
            "24": {
                "goal": [{
                    "clause": 1,
                    "scope": 1,
                    "term": "(p T1)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T1"],
                    "free": [],
                    "exprvars": []
                }
            },
            "type": "Nodes",
            "2": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(p T1)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T1"],
                    "free": [],
                    "exprvars": []
                }
            },
            "5": {
                "goal": [
                    {
                        "clause": 0,
                        "scope": 1,
                        "term": "(p T1)"
                    },
                    {
                        "clause": 1,
                        "scope": 1,
                        "term": "(p T1)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T1"],
                    "free": [],
                    "exprvars": []
                }
            },
            "80": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "81": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "82": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "83": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(p1 X2)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": ["X2"],
                    "exprvars": []
                }
            },
            "84": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "85": {
                "goal": [
                    {
                        "clause": 2,
                        "scope": 2,
                        "term": "(p1 X2)"
                    },
                    {
                        "clause": 3,
                        "scope": 2,
                        "term": "(p1 X2)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": ["X2"],
                    "exprvars": []
                }
            },
            "86": {
                "goal": [
                    {
                        "clause": -1,
                        "scope": -1,
                        "term": "(!_2)"
                    },
                    {
                        "clause": 3,
                        "scope": 2,
                        "term": "(p1 X2)"
                    }
                ],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": ["X2"],
                    "exprvars": []
                }
            },
            "87": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(true)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            }
        },
        "edges": [
            {
                "from": 2,
                "to": 5,
                "label": "CASE"
            },
            {
                "from": 5,
                "to": 23,
                "label": "PARALLEL"
            },
            {
                "from": 5,
                "to": 24,
                "label": "PARALLEL"
            },
            {
                "from": 23,
                "to": 80,
                "label": "EVAL with clause\np(b).\nand substitutionT1 -> b"
            },
            {
                "from": 23,
                "to": 81,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 24,
                "to": 83,
                "label": "EVAL with clause\np(a) :- p1(X2).\nand substitutionT1 -> a"
            },
            {
                "from": 24,
                "to": 84,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 80,
                "to": 82,
                "label": "SUCCESS"
            },
            {
                "from": 83,
                "to": 85,
                "label": "CASE"
            },
            {
                "from": 85,
                "to": 86,
                "label": "ONLY EVAL with clause\np1(b) :- !_2.\nand substitutionX2 -> b"
            },
            {
                "from": 86,
                "to": 87,
                "label": "CUT"
            },
            {
                "from": 87,
                "to": 88,
                "label": "SUCCESS"
            }
        ],
        "type": "Graph"
    }
}

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

(2)
TRUE