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	n014.star.cs.uiowa.edu
space	TCT_12

run statistics

property	value
solver	AProVE23
configuration	standard
runtime (wallclock)	1.72212219238 seconds
cpu usage	4.354606561
max memory	2.62156288E8

stage attributes

key	value
output-size	1884
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# AProVE Commit ID: 363435ff5b19173ec8a83b45cfdec073678dabcc jan-christoph 20230815 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 127 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES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