Logic Programming pair #487529161

details

property	value
status	complete
benchmark	pl8.2.1a.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	talp_plumer

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.50641393661 seconds
cpu usage	10.711711237
max memory	1.03735296E9

stage attributes

key	value
output-size	56091
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


Left Termination of the query pattern

mergesort(g,a)

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

(0) Prolog
(1) PrologToPiTRSProof [SOUND, 0 ms]
(2) PiTRS
(3) DependencyPairsProof [EQUIVALENT, 6 ms]
(4) PiDP
(5) DependencyGraphProof [EQUIVALENT, 3 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) UsableRulesProof [EQUIVALENT, 0 ms]
        (23) PiDP
        (24) PiDPToQDPProof [SOUND, 0 ms]
        (25) QDP
        (26) QDPOrderProof [EQUIVALENT, 30 ms]
        (27) QDP
        (28) PisEmptyProof [EQUIVALENT, 0 ms]
        (29) YES
    (30) PiDP
        (31) UsableRulesProof [EQUIVALENT, 0 ms]
        (32) PiDP
        (33) PiDPToQDPProof [SOUND, 0 ms]
        (34) QDP
        (35) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (36) YES
    (37) PiDP
        (38) UsableRulesProof [EQUIVALENT, 0 ms]
        (39) PiDP
        (40) PiDPToQDPProof [SOUND, 0 ms]
        (41) QDP
        (42) QDPQMonotonicMRRProof [EQUIVALENT, 34 ms]
        (43) QDP
        (44) DependencyGraphProof [EQUIVALENT, 0 ms]
        (45) TRUE


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

(0)
Obligation:
Clauses:

mergesort([], []).
mergesort(.(E, []), .(E, [])).
mergesort(.(E, .(F, U)), V) :- ','(split(U, L2, L1), ','(mergesort(.(E, L2), X), ','(mergesort(.(F, L1), Z), merge(X, Z, V)))).
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)).
split([], [], []).
split(.(E, U), .(E, V), W) :- split(U, W, V).
gt(s(X), s(Y)) :- gt(X, Y).
gt(s(X), 0).
le(s(X), s(Y)) :- le(X, Y).
le(0, s(Y)).
le(0, 0).


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

(1) PrologToPiTRSProof (SOUND)
We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes:

mergesort_in_2: (b,f)

split_in_3: (b,f,f)

merge_in_3: (b,b,f)

le_in_2: (b,b)

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