Logic Programming pair #487096656

details

property	value
status	complete
benchmark	reminder-ioi.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	talp_talp

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.06383 seconds
cpu usage	8.71141
user time	8.25469
system time	0.456713
max virtual memory	1.954372E7
max residence set size	784688.0

stage attributes

key	value
starexec-result	YES

output

YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.pl
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Left Termination of the query pattern

rem(g,a,g)

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

(0) Prolog
(1) PrologToDTProblemTransformerProof [SOUND, 39 ms]
(2) TRIPLES
(3) TriplesToPiDPProof [SOUND, 5 ms]
(4) PiDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) PiDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) PiDP
        (10) PiDPToQDPProof [SOUND, 1 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) PiDP
        (15) UsableRulesProof [EQUIVALENT, 0 ms]
        (16) PiDP
        (17) PiDPToQDPProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) PiDP
        (22) UsableRulesProof [EQUIVALENT, 0 ms]
        (23) PiDP
        (24) PiDPToQDPProof [SOUND, 0 ms]
        (25) QDP
        (26) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (27) YES
    (28) PiDP
        (29) UsableRulesProof [EQUIVALENT, 0 ms]
        (30) PiDP
        (31) PiDPToQDPProof [SOUND, 0 ms]
        (32) QDP
        (33) QDPQMonotonicMRRProof [EQUIVALENT, 17 ms]
        (34) QDP
        (35) PisEmptyProof [EQUIVALENT, 0 ms]
        (36) YES
    (37) PiDP
        (38) UsableRulesProof [EQUIVALENT, 0 ms]
        (39) PiDP
        (40) PiDPToQDPProof [SOUND, 0 ms]
        (41) QDP
        (42) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (43) 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,a,g)
----------------------------------------

(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
            ],
            [

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