details

property	value
status	complete
benchmark	2.31.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n180.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.6061 seconds
cpu usage	3.58083
user time	3.42891
system time	0.151919
max virtual memory	1.8408912E7
max residence set size	233168.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 29 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: not(true) -> false not(false) -> true odd(0) -> false odd(s(x)) -> not(odd(x)) +(x, 0) -> x +(x, s(y)) -> s(+(x, y)) +(s(x), y) -> s(+(x, y)) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:+_2 > s_1 > odd_1 > true > not_1 > 0 > false and weight map: true=2 false=2 0=1 not_1=1 odd_1=2 s_1=1 +_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: not(true) -> false not(false) -> true odd(0) -> false odd(s(x)) -> not(odd(x)) +(x, 0) -> x +(x, s(y)) -> s(+(x, y)) +(s(x), y) -> s(+(x, y)) ---------------------------------------- (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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