Logic Progr 19030 pair #381919740

details

property	value
status	complete
benchmark	divrempredef.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n046.star.cs.uiowa.edu
space	AProVE_10_prolog

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.45921206474 seconds
cpu usage	6.725873513
max memory	5.4472704E8

stage attributes

key	value
output-size	51304
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.pl /export/starexec/sandbox2/output/output_files


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


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.pl
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Left Termination of the query pattern

div(g,g,a,a)

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

(0) Prolog
(1) PrologToDTProblemTransformerProof [SOUND, 42 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 [SOUND, 0 ms]
        (11) QDP
        (12) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (13) YES
    (14) PiDP
        (15) PiDPToQDPProof [SOUND, 0 ms]
        (16) QDP
        (17) QDPQMonotonicMRRProof [EQUIVALENT, 26 ms]
        (18) QDP
        (19) DependencyGraphProof [EQUIVALENT, 0 ms]
        (20) TRUE


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

(0)
Obligation:
Clauses:

div(X, 0, Z, R) :- ','(!, fail).
div(0, Y, Z, R) :- ','(!, ','(=(Z, 0), =(R, 0))).
div(X, Y, s(Z), R) :- ','(minus(X, Y, U), ','(!, div(U, Y, Z, R))).
div(X, Y, 0, X).
minus(X, 0, X).
minus(s(X), s(Y), Z) :- minus(X, Y, Z).


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

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

{
    "root": 1,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(div X (0) Z R)",
                "(',' (!) (fail))"
            ],
            [
                "(div (0) Y Z R)",
                "(',' (!) (',' (= Z (0)) (= R (0))))"
            ],
            [
                "(div X Y (s Z) R)",
                "(',' (minus X Y U) (',' (!) (div U Y Z R)))"
            ],
            [
                "(div X Y (0) X)",
                null
            ],
            [
                "(minus X (0) X)",
                null
            ],
            [
                "(minus (s X) (s Y) Z)",
                "(minus X Y Z)"
            ]
        ]
    },
    "graph": {
        "nodes": {
            "44": {
                "goal": [{
                    "clause": -1,
                    "scope": -1,
                    "term": "(fail)"
                }],
                "kb": {

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