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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

even(g)

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

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


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

(0)
Obligation:
Clauses:

even(X) :- ','(eq(Y, f(e, f(o, Y))), c(Y, X)).
c(f(e, X1), 0).
c(f(X2, X), s(Y)) :- c(X, Y).
eq(X, X).


Query: even(g)
----------------------------------------

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

{
    "root": 2,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(even X)",
                "(',' (eq Y (f (e) (f (o) Y))) (c Y X))"
            ],
            [
                "(c (f (e) X1) (0))",
                null
            ],
            [
                "(c (f X2 X) (s Y))",
                "(c X Y)"
            ],
            [
                "(eq X X)",
                null
            ]
        ]
    },
    "graph": {
        "nodes": {
            "2": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(even T1)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T1"],
                    "free": [],
                    "exprvars": []
                }
            },
            "24": {
                "goal": [{
                    "clause": 0,
                    "scope": 1,
                    "term": "(even T1)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T1"],
                    "free": [],
                    "exprvars": []
                }
            },
            "26": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(',' (eq X11 (f (e) (f (o) X11))) (c X11 T4))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T4"],
                    "free": ["X11"],
                    "exprvars": []
                }
            },
            "27": {
                "goal": [{
                    "clause": 3,
                    "scope": 2,
                    "term": "(',' (eq X11 (f (e) (f (o) X11))) (c X11 T4))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T4"],
                    "free": ["X11"],
                    "exprvars": []
                }
            },
            "28": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "type": "Nodes"
        },
        "edges": [
            {
                "from": 2,
                "to": 24,
                "label": "CASE"
            },
            {
                "from": 24,
                "to": 26,
                "label": "ONLY EVAL with clause\neven(X10) :- ','(eq(X11, f(e, f(o, X11))), c(X11, X10)).\nand substitutionT1 -> T4,\nX10 -> T4"
            },
            {
                "from": 26,
                "to": 27,
                "label": "CASE"
            },
            {
                "from": 27,
                "to": 28,
                "label": "BACKTRACK\nfor clause: eq(X, X)because of non-unification"
            }
        ],
        "type": "Graph"
    }
}

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

(2)
TRUE