details

property	value
status	complete
benchmark	23.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n179.star.cs.uiowa.edu
space	Various_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.88255 seconds
cpu usage	3.76128
user time	3.56839
system time	0.192886
max virtual memory	1.8408912E7
max residence set size	245404.0

stage attributes

key	value
starexec-result	YES

output

YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 55 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: g(0, f(x, x)) -> x g(x, s(y)) -> g(f(x, y), 0) g(s(x), y) -> g(f(x, y), 0) g(f(x, y), 0) -> f(g(x, 0), g(y, 0)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(f(x_1, x_2)) = 1 + x_1 + x_2 POL(g(x_1, x_2)) = 2*x_1 + 2*x_2 POL(s(x_1)) = 1 + x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: g(0, f(x, x)) -> x g(f(x, y), 0) -> f(g(x, 0), g(y, 0)) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: g(x, s(y)) -> g(f(x, y), 0) g(s(x), y) -> g(f(x, y), 0) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:0 > f_2 > s_1 > g_2 and weight map: 0=2 s_1=3 f_2=0 g_2=0 The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: g(x, s(y)) -> g(f(x, y), 0) g(s(x), y) -> g(f(x, y), 0) ---------------------------------------- (4) Obligation: Q restricted rewrite system: R is empty. Q is empty. ---------------------------------------- (5) RisEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (6) YES popout

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all output return to TRS Standard