Logic Progr 19030 pair #381920014

details

property	value
status	complete
benchmark	pl4.4.3.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n057.star.cs.uiowa.edu
space	talp_plumer

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.36263394356 seconds
cpu usage	6.504210342
max memory	5.17668864E8

stage attributes

key	value
output-size	92424
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

merge(g,g,a)

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

(0) Prolog
(1) PrologToDTProblemTransformerProof [SOUND, 70 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 [EQUIVALENT, 0 ms]
        (18) QDP
        (19) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (20) YES
    (21) PiDP
        (22) PiDPToQDPProof [SOUND, 0 ms]
        (23) QDP
        (24) MRRProof [EQUIVALENT, 42 ms]
        (25) QDP
        (26) DependencyGraphProof [EQUIVALENT, 0 ms]
        (27) TRUE


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

(0)
Obligation:
Clauses:

merge(X, [], X).
merge([], X, X).
merge(.(A, X), .(B, Y), .(A, Z)) :- ','(le(A, B), merge(X, .(B, Y), Z)).
merge(.(A, X), .(B, Y), .(B, Z)) :- ','(gt(A, B), merge(.(A, X), Y, Z)).
gt(s(X), s(Y)) :- gt(X, Y).
gt(s(X), zero).
le(s(X), s(Y)) :- le(X, Y).
le(zero, s(Y)).
le(zero, zero).


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

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

{
    "root": 1,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(merge X ([]) X)",
                null
            ],
            [
                "(merge ([]) X X)",
                null
            ],
            [
                "(merge (. A X) (. B Y) (. A Z))",
                "(',' (le A B) (merge X (. B Y) Z))"
            ],
            [
                "(merge (. A X) (. B Y) (. B Z))",
                "(',' (gt A B) (merge (. A X) Y Z))"
            ],
            [
                "(gt (s X) (s Y))",
                "(gt X Y)"
            ],
            [
                "(gt (s X) (zero))",
                null
            ],
            [

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