Logic Programming pair #487529641

details

property	value
status	complete
benchmark	reminder.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	talp_talp

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.41264891624 seconds
cpu usage	6.28006976
max memory	5.69626624E8

stage attributes

key	value
output-size	52655
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.pl /export/starexec/sandbox/output/output_files


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


YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.pl
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Left Termination of the query pattern

rem(g,g,a)

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

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


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

(0)
Obligation:
Clauses:

rem(X, Y, R) :- ','(notZero(Y), ','(sub(X, Y, Z), rem(Z, Y, R))).
rem(X, Y, X) :- ','(notZero(Y), geq(X, Y)).
sub(s(X), s(Y), Z) :- sub(X, Y, Z).
sub(X, 0, X).
notZero(s(X)).
geq(s(X), s(Y)) :- geq(X, Y).
geq(X, 0).


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

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

{
    "root": 3,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(rem X Y R)",
                "(',' (notZero Y) (',' (sub X Y Z) (rem Z Y R)))"
            ],
            [
                "(rem X Y X)",
                "(',' (notZero Y) (geq X Y))"
            ],
            [
                "(sub (s X) (s Y) Z)",
                "(sub X Y Z)"
            ],
            [
                "(sub X (0) X)",
                null
            ],
            [
                "(notZero (s X))",
                null
            ],
            [
                "(geq (s X) (s Y))",
                "(geq X Y)"
            ],
            [
                "(geq X (0))",
                null

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