Logic Progr 19030 pair #381919722

details

property	value
status	complete
benchmark	divminuslinear.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n070.star.cs.uiowa.edu
space	Schneider_Kamp_08

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.22083091736 seconds
cpu usage	5.924625185
max memory	4.94092288E8

stage attributes

key	value
output-size	94308
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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)

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

(0) Prolog
(1) BuiltinConflictTransformerProof [EQUIVALENT, 0 ms]
(2) Prolog
(3) PrologToDTProblemTransformerProof [SOUND, 46 ms]
(4) TRIPLES
(5) TriplesToPiDPProof [SOUND, 0 ms]
(6) PiDP
(7) DependencyGraphProof [EQUIVALENT, 0 ms]
(8) AND
    (9) PiDP
        (10) UsableRulesProof [EQUIVALENT, 0 ms]
        (11) PiDP
        (12) PiDPToQDPProof [SOUND, 4 ms]
        (13) QDP
        (14) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (15) YES
    (16) PiDP
        (17) PiDPToQDPProof [SOUND, 0 ms]
        (18) QDP
        (19) QDPQMonotonicMRRProof [EQUIVALENT, 32 ms]
        (20) QDP
        (21) PisEmptyProof [EQUIVALENT, 0 ms]
        (22) YES


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

(0)
Obligation:
Clauses:

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


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

(1) BuiltinConflictTransformerProof (EQUIVALENT)
Renamed defined predicates conflicting with built-in predicates [PROLOG].
----------------------------------------

(2)
Obligation:
Clauses:

minus(X, Y, Z) :- ','(user_defined_=(X, 0), ','(!, user_defined_=(Z, 0))).
minus(X, Y, Z) :- ','(user_defined_=(Y, 0), ','(!, user_defined_=(Z, X))).
minus(X, Y, Z) :- ','(user_defined_=(X, s(A)), ','(user_defined_=(Y, s(B)), minus(A, B, Z))).
div(X, Y, Z) :- ','(user_defined_=(Y, 0), ','(!, fail)).
div(X, Y, Z) :- ','(user_defined_=(X, 0), ','(!, user_defined_=(Z, 0))).
div(X, Y, Z) :- ','(minus(X, Y, U), ','(div(U, Y, V), user_defined_=(Z, s(V)))).
user_defined_=(X, X).


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

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

{
    "root": 1,
    "program": {
        "directives": [],
        "clauses": [
            [
                "(minus X Y Z)",
                "(',' (user_defined_= X (0)) (',' (!) (user_defined_= Z (0))))"
            ],
            [
                "(minus X Y Z)",
                "(',' (user_defined_= Y (0)) (',' (!) (user_defined_= Z X)))"
            ],
            [
                "(minus X Y Z)",
                "(',' (user_defined_= X (s A)) (',' (user_defined_= Y (s B)) (minus A B Z)))"
            ],

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