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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

kay4(g)

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

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


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

(0)
Obligation:
Clauses:

kay4(I) :- ','(length(.(X1, .(X2, L)), I), ','(top(L), ','(mid([], L), bot(L)))).
top(L) :- ','(write(a), ','(mwrite('-', L), ','(write(b), nl))).
bot(L) :- ','(write(c), ','(mwrite('-', L), ','(write(d), nl))).
mid(X, []).
mid(X, .(X3, [])) :- ','(write('|'), ','(mwrite(' ', X), ','(write('X'), ','(mwrite(' ', X), ','(write('|'), nl))))).
mid(X, .(X4, .(X5, Y))) :- ','(write('|'), ','(mwrite(' ', X), ','(write('\\'), ','(mwrite(' ', Y), ','(write('/'), ','(mwrite(' ', X), ','(write('|'), ','(nl, ','(mid(.(X6, X), Y), ','(write('|'), ','(mwrite(' ', X), ','(write('/'), ','(mwrite(' ', Y), ','(write('\\'), ','(mwrite(' ', X), ','(write('|'), nl)))))))))))))))).
mwrite(Char, L) :- findall(X7, ','(member(X8, L), write(Char)), X9).
member(X, .(X, X10)).
member(X, .(X11, Xs)) :- member(X, Xs).


Query: kay4(g)
----------------------------------------

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

{
    "root": 1,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(kay4 I)",
                "(',' (length (. X1 (. X2 L)) I) (',' (top L) (',' (mid ([]) L) (bot L))))"
            ],
            [
                "(top L)",
                "(',' (write (a)) (',' (mwrite ('-') L) (',' (write (b)) (nl))))"
            ],
            [
                "(bot L)",
                "(',' (write (c)) (',' (mwrite ('-') L) (',' (write (d)) (nl))))"
            ],
            [
                "(mid X ([]))",
                null
            ],
            [
                "(mid X (. X3 ([])))",
                "(',' (write ('|')) (',' (mwrite (' ') X) (',' (write ('X')) (',' (mwrite (' ') X) (',' (write ('|')) (nl))))))"
            ],
            [
                "(mid X (. X4 (. X5 Y)))",
                "(',' (write ('|')) (',' (mwrite (' ') X) (',' (write ('\\\\')) (',' (mwrite (' ') Y) (',' (write ('/')) (',' (mwrite (' ') X) (',' (write ('|')) (',' (nl) (',' (mid (. X6 X) Y) (',' (write ('|')) (',' (mwrite (' ') X) (',' (write ('/')) (',' (mwrite (' ') Y) (',' (write ('\\\\')) (',' (mwrite (' ') X) (',' (write ('|')) (nl)))))))))))))))))"
            ],
            [
                "(mwrite Char L)",
                "(findall X7 (',' (member X8 L) (write Char)) X9)"
            ],
            [
                "(member X (. X X10))",
                null
            ],
            [
                "(member X (. X11 Xs))",
                "(member X Xs)"
            ]
        ]
    },
    "graph": {
        "nodes": {
            "1": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(kay4 T1)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T1"],
                    "free": [],
                    "exprvars": []
                }
            },
            "5": {
                "goal": [{
                    "clause": 0,
                    "scope": 1,
                    "term": "(kay4 T1)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T1"],
                    "free": [],
                    "exprvars": []
                }
            },
            "7": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(',' (length (. X18 (. X19 X20)) T4) (',' (top X20) (',' (mid ([]) X20) (bot X20))))"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": ["T4"],
                    "free": [
                        "X18",
                        "X19",
                        "X20"
                    ],
                    "exprvars": []
                }
            },
            "type": "Nodes",
            "10": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            }
        },
        "edges": [
            {
                "from": 1,
                "to": 5,
                "label": "CASE"
            },
            {
                "from": 5,
                "to": 7,
                "label": "ONLY EVAL with clause\nkay4(X17) :- ','(length(.(X18, .(X19, X20)), X17), ','(top(X20), ','(mid([], X20), bot(X20)))).\nand substitutionT1 -> T4,\nX17 -> T4"
            },
            {
                "from": 7,
                "to": 10,
                "label": "UNDEFINED ERROR"
            }
        ],
        "type": "Graph"
    }
}

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

(2)
TRUE