Logic Programming pair #487096690

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	n139.star.cs.uiowa.edu
space	lpexamples

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.86905 seconds
cpu usage	12.1473
user time	11.3974
system time	0.749922
max virtual memory	1.9609712E7
max residence set size	1290460.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

mergesort(g,a)

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

(0) Prolog
(1) PrologToTRSTransformerProof [SOUND, 33 ms]
(2) QTRS
(3) Overlay + Local Confluence [EQUIVALENT, 0 ms]
(4) QTRS
(5) DependencyPairsProof [EQUIVALENT, 0 ms]
(6) QDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) QDP
        (10) UsableRulesProof [EQUIVALENT, 0 ms]
        (11) QDP
        (12) QReductionProof [EQUIVALENT, 0 ms]
        (13) QDP
        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (15) YES
    (16) QDP
        (17) UsableRulesProof [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QReductionProof [EQUIVALENT, 0 ms]
        (20) QDP
        (21) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (22) YES
    (23) QDP
        (24) TransformationProof [EQUIVALENT, 0 ms]
        (25) QDP
        (26) QDPQMonotonicMRRProof [EQUIVALENT, 92 ms]
        (27) QDP
        (28) DependencyGraphProof [EQUIVALENT, 0 ms]
        (29) 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(.(X, Xs), Ys, Zs)).


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

(1) PrologToTRSTransformerProof (SOUND)
Transformed Prolog program to TRS.

{
    "root": 20,
    "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
            ],
            [
                "(split (. X Xs) (. X Ys) Zs)",
                "(split Xs Zs Ys)"
            ],
            [
                "(merge ([]) Xs Xs)",
                null
            ],
            [
                "(merge Xs ([]) Xs)",
                null
            ],
            [
                "(merge (. X Xs) (. Y Ys) (. X Zs))",

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to Logic Programming