details

property	value
status	complete
benchmark	random-472.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n048.star.cs.uiowa.edu
space	Waldmann_19

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	8.56557202339 seconds
cpu usage	15.71895652
max memory	1.290407936E9

stage attributes

key	value
output-size	6343
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 61 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) MNOCProof [EQUIVALENT, 0 ms] (9) QDP (10) UsableRulesProof [EQUIVALENT, 0 ms] (11) QDP (12) QReductionProof [EQUIVALENT, 0 ms] (13) QDP (14) QDPSizeChangeProof [EQUIVALENT, 0 ms] (15) YES (16) QDP (17) MRRProof [EQUIVALENT, 13 ms] (18) QDP (19) PisEmptyProof [EQUIVALENT, 0 ms] (20) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(a(a(a(x1)))) -> a(b(a(a(x1)))) a(b(a(a(x1)))) -> a(b(b(a(x1)))) b(b(b(a(x1)))) -> b(b(a(b(x1)))) b(a(b(a(x1)))) -> b(a(b(b(x1)))) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(a(x_1)) = 1 + x_1 POL(b(x_1)) = x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: a(b(a(a(x1)))) -> a(b(b(a(x1)))) b(a(b(a(x1)))) -> b(a(b(b(x1)))) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(a(a(a(x1)))) -> a(b(a(a(x1)))) b(b(b(a(x1)))) -> b(b(a(b(x1)))) Q is empty. ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: B(a(a(a(x1)))) -> B(a(a(x1))) B(b(b(a(x1)))) -> B(b(a(b(x1)))) B(b(b(a(x1)))) -> B(a(b(x1))) B(b(b(a(x1)))) -> B(x1) The TRS R consists of the following rules: b(a(a(a(x1)))) -> a(b(a(a(x1)))) b(b(b(a(x1)))) -> b(b(a(b(x1)))) Q is empty. popout

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