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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

max_valued(g,a)

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

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


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

(0)
Obligation:
Clauses:

max_valued(.(Head, Tail), Max) :- max_Valued(Tail, Head, Max).
max_valued([], Term, Term).
max_valued(.(Head, Tail), Term, Max) :- ','(higher_valued(Head, Term), ','(!, max_valued(Tail, Head, Max))).
max_valued(.(Head, Tail), Term, Max) :- ','(higher_valued(Term, Head), max_valued(Tail, Term, Max)).
higher_valued(X, Y) :- greater(s(X), Y).
greater(s(X1), 0).
greater(s(X), s(Y)) :- greater(X, Y).


Query: max_valued(g,a)
----------------------------------------

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

{
    "root": 2,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(max_valued (. Head Tail) Max)",
                "(max_Valued Tail Head Max)"
            ],
            [
                "(max_valued ([]) Term Term)",
                null
            ],
            [
                "(max_valued (. Head Tail) Term Max)",
                "(',' (higher_valued Head Term) (',' (!) (max_valued Tail Head Max)))"
            ],
            [
                "(max_valued (. Head Tail) Term Max)",
                "(',' (higher_valued Term Head) (max_valued Tail Term Max))"
            ],
            [
                "(higher_valued X Y)",
                "(greater (s X) Y)"
            ],
            [
                "(greater (s X1) (0))",
                null
            ],
            [
                "(greater (s X) (s Y))",
                "(greater X Y)"
            ]
        ]
    },
    "graph": {
        "nodes": {
            "22": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(max_Valued T10 T9 T12)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [
                        "T9",
                        "T10"
                    ],
                    "free": [],
                    "exprvars": []
                }
            },
            "23": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "2": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(max_valued T1 T2)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T1"],
                    "free": [],
                    "exprvars": []
                }
            },
            "4": {
                "goal": [{
                    "clause": 0,
                    "scope": 1,
                    "term": "(max_valued T1 T2)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T1"],
                    "free": [],
                    "exprvars": []
                }
            },
            "type": "Nodes",
            "40": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            }
        },
        "edges": [
            {
                "from": 2,
                "to": 4,
                "label": "CASE"
            },
            {
                "from": 4,
                "to": 22,
                "label": "EVAL with clause\nmax_valued(.(X8, X9), X10) :- max_Valued(X9, X8, X10).\nand substitutionX8 -> T9,\nX9 -> T10,\nT1 -> .(T9, T10),\nT2 -> T12,\nX10 -> T12,\nT11 -> T12"
            },
            {
                "from": 4,
                "to": 23,
                "label": "EVAL-BACKTRACK"
            },
            {
                "from": 22,
                "to": 40,
                "label": "UNDEFINED ERROR"
            }
        ],
        "type": "Graph"
    }
}

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

(2)
TRUE