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TRS Standard pair #487067972
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
n175.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
0.589663 seconds
cpu usage
1.17911
user time
0.941319
system time
0.237792
max virtual memory
1164072.0
max residence set size
68428.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: 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()) Proof: DP Processor: DPs: prime#(s(s(x))) -> prime1#(s(s(x)),s(x)) prime1#(x,s(s(y))) -> prime1#(x,s(y)) prime1#(x,s(s(y))) -> divp#(s(s(y)),x) TRS: 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()) TDG Processor: DPs: prime#(s(s(x))) -> prime1#(s(s(x)),s(x)) prime1#(x,s(s(y))) -> prime1#(x,s(y)) prime1#(x,s(s(y))) -> divp#(s(s(y)),x) TRS: 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()) graph: prime1#(x,s(s(y))) -> prime1#(x,s(y)) -> prime1#(x,s(s(y))) -> divp#(s(s(y)),x) prime1#(x,s(s(y))) -> prime1#(x,s(y)) -> prime1#(x,s(s(y))) -> prime1#(x,s(y)) prime#(s(s(x))) -> prime1#(s(s(x)),s(x)) -> prime1#(x,s(s(y))) -> divp#(s(s(y)),x) prime#(s(s(x))) -> prime1#(s(s(x)),s(x)) -> prime1#(x,s(s(y))) -> prime1#(x,s(y)) SCC Processor: #sccs: 1 #rules: 1 #arcs: 4/9 DPs: prime1#(x,s(s(y))) -> prime1#(x,s(y)) TRS: 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()) Subterm Criterion Processor: simple projection: pi(prime1#) = 1 problem: DPs: TRS: 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()) Qed
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