Logic Progr 19030 pair #381919906

details

property	value
status	complete
benchmark	mergesort.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n072.star.cs.uiowa.edu
space	prolog_mixed

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.55619215965 seconds
cpu usage	13.561304215
max memory	9.33462016E8

stage attributes

key	value
output-size	94979
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Left Termination of the query pattern

mergesort(g,a)

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

(0) Prolog
(1) PrologToDTProblemTransformerProof [SOUND, 68 ms]
(2) TRIPLES
(3) TriplesToPiDPProof [SOUND, 18 ms]
(4) PiDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) PiDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) PiDP
        (10) PiDPToQDPProof [SOUND, 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) TransformationProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) QDPQMonotonicMRRProof [EQUIVALENT, 75 ms]
        (27) QDP
        (28) UsableRulesProof [EQUIVALENT, 0 ms]
        (29) QDP
        (30) QReductionProof [EQUIVALENT, 0 ms]
        (31) QDP
        (32) QDPOrderProof [EQUIVALENT, 16 ms]
        (33) QDP
        (34) DependencyGraphProof [EQUIVALENT, 0 ms]
        (35) TRUE


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

(0)
Obligation:
Clauses:

mergesort([], []).
mergesort(.(X, []), .(X, [])).
mergesort(.(X, .(Y, Xs)), Ys) :- ','(split(.(X, .(Y, Xs)), X1s, X2s), ','(mergesort(X1s, Y1s), ','(mergesort(X2s, Y2s), merge(Y1s, Y2s, Ys)))).
split([], [], []).
split(.(X, Xs), .(X, Ys), Zs) :- split(Xs, Zs, Ys).
merge([], Xs, Xs).
merge(Xs, [], Xs).
merge(.(X, Xs), .(Y, Ys), .(X, Zs)) :- ','(=<(X, Y), merge(Xs, .(Y, Ys), Zs)).
merge(.(X, Xs), .(Y, Ys), .(Y, Zs)) :- ','(>(X, Y), merge(.(X, Xs), Ys, Zs)).


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

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

{
    "root": 2,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(mergesort ([]) ([]))",
                null
            ],
            [
                "(mergesort (. X ([])) (. X ([])))",
                null
            ],
            [
                "(mergesort (. X (. Y Xs)) Ys)",
                "(',' (split (. X (. Y Xs)) X1s X2s) (',' (mergesort X1s Y1s) (',' (mergesort X2s Y2s) (merge Y1s Y2s Ys))))"
            ],
            [
                "(split ([]) ([]) ([]))",
                null
            ],
            [

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