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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

deriv(a,g,g)

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:

d(+(U, V), X, +(DU, DV)) :- ','(!, ','(d(U, X, DU), d(V, X, DV))).
d(-(U, V), X, -(DU, DV)) :- ','(!, ','(d(U, X, DU), d(V, X, DV))).
d(*(U, V), X, +(*(DU, V), *(U, DV))) :- ','(!, ','(d(U, X, DU), d(V, X, DV))).
d(/(U, V), X, /(-(*(DU, V), *(U, DV)), ^(V, 2))) :- ','(!, ','(d(U, X, DU), d(V, X, DV))).
d(^(U, N), X, *(DU, *(N, ^(U, N1)))) :- ','(!, ','(integer(N), ','(is(N1, -(N, 1)), d(U, X, DU)))).
d(-(U), X, -(DU)) :- ','(!, d(U, X, DU)).
d(exp(U), X, *(exp(U), DU)) :- ','(!, d(U, X, DU)).
d(log(U), X, /(DU, U)) :- ','(!, d(U, X, DU)).
d(X, X, 1) :- !.
d(C, X, 0).
main :- ','(expression(X), ','(d(X, x, Y), write(Y))).
expression(+(Exp, -(Exp, *(Exp, /(Exp, *(Exp, /(Exp, Exp))))))) :- value(Exp).
value(/(+(*(3, x), -(*(4, *(exp(^(x, 3)), log(^(x, 2)))), 2)), +(-(*(3, x)), /(5, +(exp(^(x, 4)), 2))))).


Query: deriv(a,g,g)
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(1) PrologToTRSTransformerProof (SOUND)
Transformed Prolog program to TRS.

{
    "root": 3,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(d (+ U V) X (+ DU DV))",
                "(',' (!) (',' (d U X DU) (d V X DV)))"
            ],
            [
                "(d (- U V) X (- DU DV))",
                "(',' (!) (',' (d U X DU) (d V X DV)))"
            ],
            [
                "(d (* U V) X (+ (* DU V) (* U DV)))",
                "(',' (!) (',' (d U X DU) (d V X DV)))"
            ],
            [
                "(d (/ U V) X (/ (- (* DU V) (* U DV)) (^ V (2))))",
                "(',' (!) (',' (d U X DU) (d V X DV)))"
            ],
            [
                "(d (^ U N) X (* DU (* N (^ U N1))))",
                "(',' (!) (',' (integer N) (',' (is N1 (- N (1))) (d U X DU))))"
            ],
            [
                "(d (- U) X (- DU))",
                "(',' (!) (d U X DU))"
            ],
            [
                "(d (exp U) X (* (exp U) DU))",
                "(',' (!) (d U X DU))"
            ],
            [
                "(d (log U) X (/ DU U))",
                "(',' (!) (d U X DU))"
            ],
            [
                "(d X X (1))",
                "(!)"
            ],
            [
                "(d C X (0))",
                null
            ],
            [
                "(main)",
                "(',' (expression X) (',' (d X (x) Y) (write Y)))"
            ],
            [
                "(expression (+ Exp (- Exp (* Exp (/ Exp (* Exp (/ Exp Exp)))))))",
                "(value Exp)"
            ],
            [
                "(value (/ (+ (* (3) (x)) (- (* (4) (* (exp (^ (x) (3))) (log (^ (x) (2))))) (2))) (+ (- (* (3) (x))) (/ (5) (+ (exp (^ (x) (4))) (2))))))",
                null
            ]
        ]
    },
    "graph": {
        "nodes": {
            "3": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(deriv T1 T2 T3)"
                }],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [
                        "T2",
                        "T3"
                    ],
                    "free": [],
                    "exprvars": []
                }
            },
            "4": {
                "goal": [],
                "kb": {
                    "nonunifying": [],
                    "intvars": {},
                    "arithmetic": {
                        "type": "PlainIntegerRelationState",
                        "relations": []
                    },
                    "ground": [],
                    "free": [],
                    "exprvars": []
                }
            },
            "type": "Nodes"
        },
        "edges": [{
            "from": 3,
            "to": 4,
            "label": "UNDEFINED ERROR"
        }],
        "type": "Graph"
    }
}

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

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

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(3) RisEmptyProof (EQUIVALENT)
The TRS R is empty. Hence, termination is trivially proven.
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(4)
YES