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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

n()

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

(0) Prolog
(1) PrologToTRSTransformerProof [SOUND, 0 ms]
(2) QTRS
(3) RisEmptyProof [EQUIVALENT, 0 ms]
(4) YES


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(0)
Obligation:
Clauses:

n :- ','(=(X, f(1, f(0, X))), g(X)).
g(f(X, f(X, X1))) :- !.
g(f(X2, X)) :- g(X).


Query: n()
----------------------------------------

(1) PrologToTRSTransformerProof (SOUND)
Transformed Prolog program to TRS.

{
    "root": 5,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(n)",
                "(',' (= X (f (1) (f (0) X))) (g X))"
            ],
            [
                "(g (f X (f X X1)))",
                "(!)"
            ],
            [
                "(g (f X2 X))",
                "(g X)"
            ]
        ]
    },
    "graph": {
        "nodes": {
            "12": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "5": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(n)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "6": {
                "goal": [{
                    "clause": 0,
                    "scope": 1,
                    "term": "(n)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "8": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(',' (= X4 (f (1) (f (0) X4))) (g X4))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": ["X4"],
                    "exprvars": []
                }
            },
            "type": "Nodes"
        },
        "edges": [
            {
                "from": 5,
                "to": 6,
                "label": "CASE"
            },
            {
                "from": 6,
                "to": 8,
                "label": "ONLY EVAL with clause\nn :- ','(=(X4, f(1, f(0, X4))), g(X4)).\nand substitution"
            },
            {
                "from": 8,
                "to": 12,
                "label": "UNIFY-FAIL\nbecause of non-unification"
            }
        ],
        "type": "Graph"
    }
}

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

(2)
Obligation:
Q restricted rewrite system:
R is empty.
Q is empty.

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

(3) RisEmptyProof (EQUIVALENT)
The TRS R is empty. Hence, termination is trivially proven.
----------------------------------------

(4)
YES