details

property	value
status	complete
benchmark	ordered.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	BCGGV05

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.18242 seconds
cpu usage	5.16241
user time	4.8957
system time	0.266708
max virtual memory	1.907778E7
max residence set size	415992.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.pl # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Left Termination of the query pattern ordered(g) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToPiTRSProof [SOUND, 0 ms] (2) PiTRS (3) DependencyPairsProof [EQUIVALENT, 1 ms] (4) PiDP (5) DependencyGraphProof [EQUIVALENT, 0 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) MRRProof [EQUIVALENT, 18 ms] (20) QDP (21) PisEmptyProof [EQUIVALENT, 0 ms] (22) YES ---------------------------------------- (0) Obligation: Clauses: ordered([]). ordered(.(X1, [])). ordered(.(X, .(Y, Xs))) :- ','(less(X, s(Y)), ordered(.(Y, Xs))). less(0, s(X2)). less(s(X), s(Y)) :- less(X, Y). Query: ordered(g) ---------------------------------------- (1) PrologToPiTRSProof (SOUND) We use the technique of [TOCL09]. With regard to the inferred argument filtering the predicates were used in the following modes: ordered_in_1: (b) less_in_2: (b,b) Transforming Prolog into the following Term Rewriting System: Pi-finite rewrite system: The TRS R consists of the following rules: ordered_in_g([]) -> ordered_out_g([]) ordered_in_g(.(X1, [])) -> ordered_out_g(.(X1, [])) ordered_in_g(.(X, .(Y, Xs))) -> U1_g(X, Y, Xs, less_in_gg(X, s(Y))) less_in_gg(0, s(X2)) -> less_out_gg(0, s(X2)) less_in_gg(s(X), s(Y)) -> U3_gg(X, Y, less_in_gg(X, Y)) U3_gg(X, Y, less_out_gg(X, Y)) -> less_out_gg(s(X), s(Y)) U1_g(X, Y, Xs, less_out_gg(X, s(Y))) -> U2_g(X, Y, Xs, ordered_in_g(.(Y, Xs))) U2_g(X, Y, Xs, ordered_out_g(.(Y, Xs))) -> ordered_out_g(.(X, .(Y, Xs))) Pi is empty. Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog ---------------------------------------- (2) Obligation: Pi-finite rewrite system: The TRS R consists of the following rules: ordered_in_g([]) -> ordered_out_g([]) ordered_in_g(.(X1, [])) -> ordered_out_g(.(X1, [])) ordered_in_g(.(X, .(Y, Xs))) -> U1_g(X, Y, Xs, less_in_gg(X, s(Y))) less_in_gg(0, s(X2)) -> less_out_gg(0, s(X2)) less_in_gg(s(X), s(Y)) -> U3_gg(X, Y, less_in_gg(X, Y)) U3_gg(X, Y, less_out_gg(X, Y)) -> less_out_gg(s(X), s(Y)) U1_g(X, Y, Xs, less_out_gg(X, s(Y))) -> U2_g(X, Y, Xs, ordered_in_g(.(Y, Xs))) U2_g(X, Y, Xs, ordered_out_g(.(Y, Xs))) -> ordered_out_g(.(X, .(Y, Xs))) Pi is empty. ---------------------------------------- popout

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

job log

popout

actions

all output return to Logic Programming