Logic Progr 19030 pair #381919948

details

property	value
status	complete
benchmark	qsort.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n074.star.cs.uiowa.edu
space	talp_talp

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.88994193077 seconds
cpu usage	10.956028623
max memory	7.60635392E8

stage attributes

key	value
output-size	52066
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

qs(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, 3 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) 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 [EQUIVALENT, 0 ms]
        (25) QDP
        (26) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (27) YES
    (28) PiDP
        (29) UsableRulesProof [EQUIVALENT, 0 ms]
        (30) PiDP
        (31) PiDPToQDPProof [SOUND, 0 ms]
        (32) QDP
        (33) QDPSizeChangeProof [EQUIVALENT, 0 ms]
        (34) YES
    (35) PiDP
        (36) PiDPToQDPProof [SOUND, 0 ms]
        (37) QDP
        (38) QDPQMonotonicMRRProof [EQUIVALENT, 92 ms]
        (39) QDP
        (40) DependencyGraphProof [EQUIVALENT, 0 ms]
        (41) TRUE


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

(0)
Obligation:
Clauses:

qs([], []).
qs(cons(X, L), S) :- ','(split(L, X, L1, L2), ','(qs(L1, S1), ','(qs(L2, S2), append(S1, cons(X, S2), S)))).
append([], L, L).
append(cons(X, L1), L2, cons(X, L3)) :- append(L1, L2, L3).
split([], X, [], []).
split(cons(X, L), Y, cons(X, L1), L2) :- ','(less(X, Y), split(L, Y, L1, L2)).
split(cons(X, L), Y, L1, cons(X, L2)) :- ','(geq(X, Y), split(L, Y, L1, L2)).
less(0, s(X)).
less(s(X), s(Y)) :- less(X, Y).
geq(X, X).
geq(s(X), 0).
geq(s(X), s(Y)) :- geq(X, Y).


Query: qs(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:

qs_in_2: (b,f)

split_in_4: (b,b,f,f)

less_in_2: (b,b)

geq_in_2: (b,b)

append_in_3: (b,b,f)

Transforming Prolog into the following Term Rewriting System:

Pi-finite rewrite system:

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to Logic Progr 19030