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TRS Standard pair #487067973
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
n073.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.73428 seconds
cpu usage
3.71069
user time
3.55597
system time
0.154722
max virtual memory
1.8408912E7
max residence set size
237248.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 54 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4)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
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