details

property	value
status	complete
benchmark	normal.pl
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n084.star.cs.uiowa.edu
space	talp_talp

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.19831204414 seconds
cpu usage	5.11947264
max memory	4.87706624E8

stage attributes

key	value
output-size	14720
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Left Termination of the query pattern normal(g,a) w.r.t. the given Prolog program could successfully be proven: (0) Prolog (1) PrologToPiTRSProof [SOUND,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, 10 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 [SOUND, 0 ms] (18) QDP (19) MRRProof [EQUIVALENT, 14 ms] (20) QDP (21) PisEmptyProof [EQUIVALENT, 0 ms] (22) YES ---------------------------------------- (0) Obligation: Clauses: normal(F, N) :- ','(rewrite(F, F1), normal(F1, N)). normal(F, F). rewrite(op(op(A, B), C), op(A, op(B, C))). rewrite(op(A, op(B, C)), op(A, L)) :- rewrite(op(B, C), L). Query: normal(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: normal_in_2: (b,f) rewrite_in_2: (b,f) Transforming Prolog into the following Term Rewriting System: Pi-finite rewrite system: The TRS R consists of the following rules: normal_in_ga(F, N) -> U1_ga(F, N, rewrite_in_ga(F, F1)) rewrite_in_ga(op(op(A, B), C), op(A, op(B, C))) -> rewrite_out_ga(op(op(A, B), C), op(A, op(B, C))) rewrite_in_ga(op(A, op(B, C)), op(A, L)) -> U3_ga(A, B, C, L, rewrite_in_ga(op(B, C), L)) U3_ga(A, B, C, L, rewrite_out_ga(op(B, C), L)) -> rewrite_out_ga(op(A, op(B, C)), op(A, L)) U1_ga(F, N, rewrite_out_ga(F, F1)) -> U2_ga(F, N, normal_in_ga(F1, N)) normal_in_ga(F, F) -> normal_out_ga(F, F) U2_ga(F, N, normal_out_ga(F1, N)) -> normal_out_ga(F, N) The argument filtering Pi contains the following mapping: normal_in_ga(x1, x2) = normal_in_ga(x1) U1_ga(x1, x2, x3) = U1_ga(x3) rewrite_in_ga(x1, x2) = rewrite_in_ga(x1) op(x1, x2) = op(x1, x2) rewrite_out_ga(x1, x2) = rewrite_out_ga(x2) U3_ga(x1, x2, x3, x4, x5) = U3_ga(x1, x5) U2_ga(x1, x2, x3) = U2_ga(x3) normal_out_ga(x1, x2) = normal_out_ga(x2) Infinitary Constructor Rewriting Termination of PiTRS implies Termination of Prolog popout

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