details

property	value
status	complete
benchmark	polycounter-5.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n191.star.cs.uiowa.edu
space	TCT_12

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.74647 seconds
cpu usage	3.84291
user time	3.68842
system time	0.154497
max virtual memory	1.834722E7
max residence set size	235528.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 81 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(s(x1), x2, x3, x4, x5) -> f(x1, x2, x3, x4, x5) f(0, s(x2), x3, x4, x5) -> f(x2, x2, x3, x4, x5) f(0, 0, s(x3), x4, x5) -> f(x3, x3, x3, x4, x5) f(0, 0, 0, s(x4), x5) -> f(x4, x4, x4, x4, x5) f(0, 0, 0, 0, s(x5)) -> f(x5, x5, x5, x5, x5) f(0, 0, 0, 0, 0) -> 0 Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: [f_5, s_1, 0] Status: f_5: [5,4,3,2,1] s_1: multiset status 0: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f(s(x1), x2, x3, x4, x5) -> f(x1, x2, x3, x4, x5) f(0, s(x2), x3, x4, x5) -> f(x2, x2, x3, x4, x5) f(0, 0, s(x3), x4, x5) -> f(x3, x3, x3, x4, x5) f(0, 0, 0, s(x4), x5) -> f(x4, x4, x4, x4, x5) f(0, 0, 0, 0, s(x5)) -> f(x5, x5, x5, x5, x5) f(0, 0, 0, 0, 0) -> 0 ---------------------------------------- (2) Obligation: Q restricted rewrite system: R is empty. Q is empty. ---------------------------------------- (3) RisEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (4) YES popout

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all output return to TRS Standard