Logic Progr 19030 pair #381919749

details

property	value
status	complete
benchmark	qsortapp.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n077.star.cs.uiowa.edu
space	talp_maria

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.36552405357 seconds
cpu usage	9.470796543
max memory	6.47098368E8

stage attributes

key	value
output-size	35596
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

qsort(g,a)

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

(0) Prolog
(1) CutEliminatorProof [SOUND, 0 ms]
(2) Prolog
(3) UndefinedPredicateHandlerProof [SOUND, 0 ms]
(4) Prolog
(5) PrologToPiTRSProof [SOUND, 12 ms]
(6) PiTRS
(7) DependencyPairsProof [EQUIVALENT, 0 ms]
(8) PiDP
(9) DependencyGraphProof [EQUIVALENT, 0 ms]
(10) AND
    (11) PiDP
        (12) UsableRulesProof [EQUIVALENT, 0 ms]
        (13) PiDP
        (14) PiDPToQDPProof [SOUND, 13 ms]
        (15) QDP
        (16) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (17) YES
    (18) PiDP
        (19) UsableRulesProof [EQUIVALENT, 0 ms]
        (20) PiDP
        (21) PiDPToQDPProof [SOUND, 0 ms]
        (22) QDP
        (23) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (24) YES
    (25) PiDP
        (26) PiDPToQDPProof [SOUND, 0 ms]
        (27) QDP
        (28) QDPOrderProof [EQUIVALENT, 57 ms]
        (29) QDP
        (30) DependencyGraphProof [EQUIVALENT, 0 ms]
        (31) TRUE


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

(0)
Obligation:
Clauses:

qsort(.(X, L), R) :- ','(partition(L, X, L1, L2), ','(qsort(L2, R2), ','(qsort(L1, R1), append(R1, .(X, R2), R)))).
qsort([], []).
partition([], X1, [], []).
partition(.(E, R), C, .(E, Left1), Right) :- ','(<(E, C), ','(!, partition(R, C, Left1, Right))).
partition(.(E, R), C, Left, .(E, Right1)) :- partition(R, C, Left, Right1).
append([], X, X).
append(.(H, X), Y, .(H, Z)) :- append(X, Y, Z).


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

(1) CutEliminatorProof (SOUND)
Eliminated all cuts by simply ignoring them[PROLOG].
----------------------------------------

(2)
Obligation:
Clauses:

qsort(.(X, L), R) :- ','(partition(L, X, L1, L2), ','(qsort(L2, R2), ','(qsort(L1, R1), append(R1, .(X, R2), R)))).
qsort([], []).
partition([], X1, [], []).
partition(.(E, R), C, .(E, Left1), Right) :- ','(<(E, C), partition(R, C, Left1, Right)).
partition(.(E, R), C, Left, .(E, Right1)) :- partition(R, C, Left, Right1).
append([], X, X).
append(.(H, X), Y, .(H, Z)) :- append(X, Y, Z).


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

(3) UndefinedPredicateHandlerProof (SOUND)
Added facts for all undefined predicates [PROLOG].
----------------------------------------

(4)
Obligation:
Clauses:

qsort(.(X, L), R) :- ','(partition(L, X, L1, L2), ','(qsort(L2, R2), ','(qsort(L1, R1), append(R1, .(X, R2), R)))).
qsort([], []).
partition([], X1, [], []).

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