Logic Programming pair #487096226

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	n140.star.cs.uiowa.edu
space	talp_plumer

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.36037 seconds
cpu usage	6.24867
user time	5.9394
system time	0.309272
max virtual memory	3.765404E7
max residence set size	558148.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

merge(g,g,a)

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

(0) Prolog
(1) PrologToDTProblemTransformerProof [SOUND, 39 ms]
(2) TRIPLES
(3) TriplesToPiDPProof [SOUND, 19 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, 9 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
            ],
            [
                "(le (s X) (s Y))",
                "(le X Y)"
            ],
            [
                "(le (zero) (s Y))",
                null

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