Logic Progr 19030 pair #381919809

details

property	value
status	complete
benchmark	divminus.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n074.star.cs.uiowa.edu
space	Schneider_Kamp_08

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.22123289108 seconds
cpu usage	5.742692126
max memory	5.14904064E8

stage attributes

key	value
output-size	44670
starexec-result	YES

output

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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

div(g,g,a)

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

(0) Prolog
(1) BuiltinConflictTransformerProof [EQUIVALENT, 0 ms]
(2) Prolog
(3) PrologToDTProblemTransformerProof [SOUND, 0 ms]
(4) TRIPLES
(5) TriplesToPiDPProof [SOUND, 0 ms]
(6) PiDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) PiDP
        (10) UsableRulesProof [EQUIVALENT, 0 ms]
        (11) PiDP
        (12) PiDPToQDPProof [SOUND, 15 ms]
        (13) QDP
        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (15) YES
    (16) PiDP
        (17) PiDPToQDPProof [SOUND, 0 ms]
        (18) QDP
        (19) QDPQMonotonicMRRProof [EQUIVALENT, 27 ms]
        (20) QDP
        (21) DependencyGraphProof [EQUIVALENT, 0 ms]
        (22) TRUE


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

(0)
Obligation:
Clauses:

div(X, 0, Z) :- ','(!, fail).
div(0, Y, Z) :- ','(!, =(Z, 0)).
div(X, Y, s(Z)) :- ','(minus(X, Y, U), div(U, Y, Z)).
minus(0, Y, 0).
minus(X, 0, X).
minus(s(X), s(Y), Z) :- minus(X, Y, Z).
=(X, X).


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

(1) BuiltinConflictTransformerProof (EQUIVALENT)
Renamed defined predicates conflicting with built-in predicates [PROLOG].
----------------------------------------

(2)
Obligation:
Clauses:

div(X, 0, Z) :- ','(!, fail).
div(0, Y, Z) :- ','(!, user_defined_=(Z, 0)).
div(X, Y, s(Z)) :- ','(minus(X, Y, U), div(U, Y, Z)).
minus(0, Y, 0).
minus(X, 0, X).
minus(s(X), s(Y), Z) :- minus(X, Y, Z).
user_defined_=(X, X).


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

(3) PrologToDTProblemTransformerProof (SOUND)
Built DT problem from termination graph DT10.

{
    "root": 1,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(div X (0) Z)",
                "(',' (!) (fail))"
            ],
            [
                "(div (0) Y Z)",
                "(',' (!) (user_defined_= Z (0)))"
            ],
            [
                "(div X Y (s Z))",
                "(',' (minus X Y U) (div U Y Z))"
            ],

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