details

property	value
status	complete
benchmark	p.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n027.star.cs.uiowa.edu
space	SGST06

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.6504740715 seconds
cpu usage	11.281537833
max memory	1.303769088E9

stage attributes

key	value
output-size	14886
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Left Termination of the query pattern p(g) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToPiTRSProof [SOUND, 0 ms] (2) PiTRS (3) DependencyPairsProof [EQUIVALENT, 4 ms] (4) PiDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) PiDP (7) PiDPToQDPProof [SOUND, 24 ms] (8) QDP (9) QDPQMonotonicMRRProof [EQUIVALENT, 37 ms] (10) QDP (11) QDPQMonotonicMRRProof [EQUIVALENT, 35 ms] (12) QDP (13) DependencyGraphProof [EQUIVALENT, 0 ms] (14) QDP (15) UsableRulesProof [EQUIVALENT, 0 ms] (16) QDP (17) QReductionProof [EQUIVALENT, 0 ms] (18) QDP (19) UsableRulesReductionPairsProof [EQUIVALENT, 2 ms] (20) QDP (21) PisEmptyProof [EQUIVALENT, 0 ms] (22) YES ---------------------------------------- (0) Obligation: Clauses: p(cons(X, nil)). p(cons(s(s(X)), cons(Y, Xs))) :- ','(p(cons(X, cons(Y, Xs))), p(cons(s(s(s(s(Y)))), Xs))). p(cons(0, Xs)) :- p(Xs). Query: p(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: p_in_1: (b) Transforming Prolog into the following Term Rewriting System: Pi-finite rewrite system: The TRS R consists of the following rules: p_in_g(cons(X, nil)) -> p_out_g(cons(X, nil)) p_in_g(cons(s(s(X)), cons(Y, Xs))) -> U1_g(X, Y, Xs, p_in_g(cons(X, cons(Y, Xs)))) p_in_g(cons(0, Xs)) -> U3_g(Xs, p_in_g(Xs)) U3_g(Xs, p_out_g(Xs)) -> p_out_g(cons(0, Xs)) U1_g(X, Y, Xs, p_out_g(cons(X, cons(Y, Xs)))) -> U2_g(X, Y, Xs, p_in_g(cons(s(s(s(s(Y)))), Xs))) U2_g(X, Y, Xs, p_out_g(cons(s(s(s(s(Y)))), Xs))) -> p_out_g(cons(s(s(X)), cons(Y, Xs))) The argument filtering Pi contains the following mapping: p_in_g(x1) = p_in_g(x1) cons(x1, x2) = cons(x1, x2) nil = nil p_out_g(x1) = p_out_g s(x1) = s(x1) U1_g(x1, x2, x3, x4) = U1_g(x2, x3, x4) 0 = 0 U3_g(x1, x2) = U3_g(x2) U2_g(x1, x2, x3, x4) = U2_g(x4) Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog popout

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actions

all output return to Logic Progr 19030