details

property	value
status	complete
benchmark	2.29.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n087.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	2.16653704643 seconds
cpu usage	5.540099382
max memory	4.74570752E8

stage attributes

key	value
output-size	2211
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 106 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: prime(0) -> false prime(s(0)) -> false prime(s(s(x))) -> prime1(s(s(x)), s(x)) prime1(x, 0) -> false prime1(x, s(0)) -> true prime1(x, s(s(y))) -> and(not(divp(s(s(y)), x)), prime1(x, s(y))) divp(x, y) -> =(rem(x, y), 0) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: prime/1(YES) 0/0) false/0) s/1(YES) prime1/2(YES,YES) true/0) and/2(YES,YES) not/1)YES( divp/2(YES,YES) =/2(YES,YES) rem/2(YES,YES) Quasi precedence: prime_1 > [false, prime1_2, true] > s_1 > [=_2, rem_2] prime_1 > [false, prime1_2, true] > and_2 > [=_2, rem_2] prime_1 > [false, prime1_2, true] > divp_2 > 0 > [=_2, rem_2] Status: prime_1: multiset status 0: multiset status false: multiset status s_1: [1] prime1_2: [1,2] true: multiset status and_2: [1,2] divp_2: multiset status =_2: [1,2] rem_2: [1,2] With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: prime(0) -> false prime(s(0)) -> false prime(s(s(x))) -> prime1(s(s(x)), s(x)) prime1(x, 0) -> false prime1(x, s(0)) -> true prime1(x, s(s(y))) -> and(not(divp(s(s(y)), x)), prime1(x, s(y))) divp(x, y) -> =(rem(x, y), 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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