Logic Programming pair #487096140

details

property	value
status	complete
benchmark	mergesort_ap.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n144.star.cs.uiowa.edu
space	talp_apt

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	6.1105 seconds
cpu usage	20.2137
user time	19.1024
system time	1.11136
max virtual memory	1.988438E7
max residence set size	2193472.0

stage attributes

key	value
starexec-result	YES

output

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Left Termination of the query pattern

mergesort(g,a,a)

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

(0) Prolog
(1) PrologToTRSTransformerProof [SOUND, 79 ms]
(2) QTRS
(3) DependencyPairsProof [EQUIVALENT, 8 ms]
(4) QDP
(5) DependencyGraphProof [EQUIVALENT, 0 ms]
(6) AND
    (7) QDP
        (8) UsableRulesProof [EQUIVALENT, 0 ms]
        (9) QDP
        (10) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (11) YES
    (12) QDP
        (13) UsableRulesProof [EQUIVALENT, 0 ms]
        (14) QDP
        (15) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (16) YES
    (17) QDP
        (18) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (19) YES
    (20) QDP
        (21) UsableRulesProof [EQUIVALENT, 0 ms]
        (22) QDP
        (23) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (24) YES
    (25) QDP
        (26) QDPOrderProof [EQUIVALENT, 305 ms]
        (27) QDP
        (28) DependencyGraphProof [EQUIVALENT, 0 ms]
        (29) TRUE


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

(0)
Obligation:
Clauses:

mergesort([], [], Ls).
mergesort(.(X, []), .(X, []), Ls).
mergesort(.(X, .(Y, Xs)), Ys, .(H, Ls)) :- ','(split(.(X, .(Y, Xs)), X1s, X2s, .(H, Ls)), ','(mergesort(X1s, Y1s, Ls), ','(mergesort(X2s, Y2s, Ls), merge(Y1s, Y2s, Ys, .(H, Ls))))).
split([], [], [], Ls).
split(.(X, Xs), .(X, Ys), Zs, .(H, Ls)) :- split(Xs, Zs, Ys, Ls).
merge([], Xs, Xs, Ls).
merge(Xs, [], Xs, Ls).
merge(.(X, Xs), .(Y, Ys), .(X, Zs), .(H, Ls)) :- ','(le(X, Y), merge(Xs, .(Y, Ys), Zs, Ls)).
merge(.(X, Xs), .(Y, Ys), .(Y, Zs), .(H, Ls)) :- ','(gt(X, Y), merge(.(X, Xs), Ys, Zs, Ls)).
gt(s(X), s(Y)) :- gt(X, Y).
gt(s(0), 0).
le(s(X), s(Y)) :- le(X, Y).
le(0, s(0)).
le(0, 0).


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

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

{
    "root": 1,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(mergesort ([]) ([]) Ls)",
                null
            ],
            [
                "(mergesort (. X ([])) (. X ([])) Ls)",
                null
            ],
            [
                "(mergesort (. X (. Y Xs)) Ys (. H Ls))",
                "(',' (split (. X (. Y Xs)) X1s X2s (. H Ls)) (',' (mergesort X1s Y1s Ls) (',' (mergesort X2s Y2s Ls) (merge Y1s Y2s Ys (. H Ls)))))"
            ],
            [
                "(split ([]) ([]) ([]) Ls)",
                null
            ],
            [
                "(split (. X Xs) (. X Ys) Zs (. H Ls))",
                "(split Xs Zs Ys Ls)"
            ],
            [
                "(merge ([]) Xs Xs Ls)",
                null
            ],

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