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TRS Standard pair #487067974
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
n191.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0184589 seconds
cpu usage
0.018835
user time
0.009295
system time
0.00954
max virtual memory
113188.0
max residence set size
5272.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES divp(x:S,y:S) -> =(rem(x:S,y:S),0) prime(0) -> ffalse prime(s(0)) -> ffalse prime(s(s(x:S))) -> prime1(s(s(x:S)),s(x:S)) prime1(x:S,0) -> ffalse prime1(x:S,s(0)) -> ttrue prime1(x:S,s(s(y:S))) -> and(not(divp(s(s(y:S)),x:S)),prime1(x:S,s(y:S))) ) Problem 1: Innermost Equivalent Processor: -> Rules: divp(x:S,y:S) -> =(rem(x:S,y:S),0) prime(0) -> ffalse prime(s(0)) -> ffalse prime(s(s(x:S))) -> prime1(s(s(x:S)),s(x:S)) prime1(x:S,0) -> ffalse prime1(x:S,s(0)) -> ttrue prime1(x:S,s(s(y:S))) -> and(not(divp(s(s(y:S)),x:S)),prime1(x:S,s(y:S))) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: PRIME(s(s(x:S))) -> PRIME1(s(s(x:S)),s(x:S)) PRIME1(x:S,s(s(y:S))) -> DIVP(s(s(y:S)),x:S) PRIME1(x:S,s(s(y:S))) -> PRIME1(x:S,s(y:S)) -> Rules: divp(x:S,y:S) -> =(rem(x:S,y:S),0) prime(0) -> ffalse prime(s(0)) -> ffalse prime(s(s(x:S))) -> prime1(s(s(x:S)),s(x:S)) prime1(x:S,0) -> ffalse prime1(x:S,s(0)) -> ttrue prime1(x:S,s(s(y:S))) -> and(not(divp(s(s(y:S)),x:S)),prime1(x:S,s(y:S))) Problem 1: SCC Processor: -> Pairs: PRIME(s(s(x:S))) -> PRIME1(s(s(x:S)),s(x:S)) PRIME1(x:S,s(s(y:S))) -> DIVP(s(s(y:S)),x:S) PRIME1(x:S,s(s(y:S))) -> PRIME1(x:S,s(y:S)) -> Rules: divp(x:S,y:S) -> =(rem(x:S,y:S),0) prime(0) -> ffalse prime(s(0)) -> ffalse prime(s(s(x:S))) -> prime1(s(s(x:S)),s(x:S)) prime1(x:S,0) -> ffalse prime1(x:S,s(0)) -> ttrue prime1(x:S,s(s(y:S))) -> and(not(divp(s(s(y:S)),x:S)),prime1(x:S,s(y:S))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: PRIME1(x:S,s(s(y:S))) -> PRIME1(x:S,s(y:S)) ->->-> Rules: divp(x:S,y:S) -> =(rem(x:S,y:S),0) prime(0) -> ffalse prime(s(0)) -> ffalse prime(s(s(x:S))) -> prime1(s(s(x:S)),s(x:S)) prime1(x:S,0) -> ffalse prime1(x:S,s(0)) -> ttrue prime1(x:S,s(s(y:S))) -> and(not(divp(s(s(y:S)),x:S)),prime1(x:S,s(y:S))) Problem 1: Subterm Processor: -> Pairs: PRIME1(x:S,s(s(y:S))) -> PRIME1(x:S,s(y:S)) -> Rules: divp(x:S,y:S) -> =(rem(x:S,y:S),0) prime(0) -> ffalse prime(s(0)) -> ffalse prime(s(s(x:S))) -> prime1(s(s(x:S)),s(x:S)) prime1(x:S,0) -> ffalse prime1(x:S,s(0)) -> ttrue prime1(x:S,s(s(y:S))) -> and(not(divp(s(s(y:S)),x:S)),prime1(x:S,s(y:S))) ->Projection: pi(PRIME1) = 2 Problem 1: SCC Processor: -> Pairs: Empty -> Rules: divp(x:S,y:S) -> =(rem(x:S,y:S),0) prime(0) -> ffalse prime(s(0)) -> ffalse prime(s(s(x:S))) -> prime1(s(s(x:S)),s(x:S)) prime1(x:S,0) -> ffalse
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