details

property	value
status	complete
benchmark	perfect.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n074.star.cs.uiowa.edu
space	Mixed_TRS

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.0201831 seconds
cpu usage	0.02059
user time	0.006538
system time	0.014052
max virtual memory	113188.0
max residence set size	5308.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S u:S x:S y:S z:S) (RULES f(0,y:S,0,u:S) -> ttrue f(0,y:S,s(z:S),u:S) -> ffalse f(s(x:S),0,z:S,u:S) -> f(x:S,u:S,minus(z:S,s(x:S)),u:S) f(s(x:S),s(y:S),z:S,u:S) -> if(le(x:S,y:S),f(s(x:S),minus(y:S,x:S),z:S,u:S),f(x:S,u:S,z:S,u:S)) perfectp(0) -> ffalse perfectp(s(x:S)) -> f(x:S,s(0),s(x:S),s(x:S)) ) Problem 1: Innermost Equivalent Processor: -> Rules: f(0,y:S,0,u:S) -> ttrue f(0,y:S,s(z:S),u:S) -> ffalse f(s(x:S),0,z:S,u:S) -> f(x:S,u:S,minus(z:S,s(x:S)),u:S) f(s(x:S),s(y:S),z:S,u:S) -> if(le(x:S,y:S),f(s(x:S),minus(y:S,x:S),z:S,u:S),f(x:S,u:S,z:S,u:S)) perfectp(0) -> ffalse perfectp(s(x:S)) -> f(x:S,s(0),s(x:S),s(x:S)) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: F(s(x:S),0,z:S,u:S) -> F(x:S,u:S,minus(z:S,s(x:S)),u:S) F(s(x:S),s(y:S),z:S,u:S) -> F(x:S,u:S,z:S,u:S) PERFECTP(s(x:S)) -> F(x:S,s(0),s(x:S),s(x:S)) -> Rules: f(0,y:S,0,u:S) -> ttrue f(0,y:S,s(z:S),u:S) -> ffalse f(s(x:S),0,z:S,u:S) -> f(x:S,u:S,minus(z:S,s(x:S)),u:S) f(s(x:S),s(y:S),z:S,u:S) -> if(le(x:S,y:S),f(s(x:S),minus(y:S,x:S),z:S,u:S),f(x:S,u:S,z:S,u:S)) perfectp(0) -> ffalse perfectp(s(x:S)) -> f(x:S,s(0),s(x:S),s(x:S)) Problem 1: SCC Processor: -> Pairs: F(s(x:S),0,z:S,u:S) -> F(x:S,u:S,minus(z:S,s(x:S)),u:S) F(s(x:S),s(y:S),z:S,u:S) -> F(x:S,u:S,z:S,u:S) PERFECTP(s(x:S)) -> F(x:S,s(0),s(x:S),s(x:S)) -> Rules: f(0,y:S,0,u:S) -> ttrue f(0,y:S,s(z:S),u:S) -> ffalse f(s(x:S),0,z:S,u:S) -> f(x:S,u:S,minus(z:S,s(x:S)),u:S) f(s(x:S),s(y:S),z:S,u:S) -> if(le(x:S,y:S),f(s(x:S),minus(y:S,x:S),z:S,u:S),f(x:S,u:S,z:S,u:S)) perfectp(0) -> ffalse perfectp(s(x:S)) -> f(x:S,s(0),s(x:S),s(x:S)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(s(x:S),0,z:S,u:S) -> F(x:S,u:S,minus(z:S,s(x:S)),u:S) F(s(x:S),s(y:S),z:S,u:S) -> F(x:S,u:S,z:S,u:S) ->->-> Rules: f(0,y:S,0,u:S) -> ttrue f(0,y:S,s(z:S),u:S) -> ffalse f(s(x:S),0,z:S,u:S) -> f(x:S,u:S,minus(z:S,s(x:S)),u:S) f(s(x:S),s(y:S),z:S,u:S) -> if(le(x:S,y:S),f(s(x:S),minus(y:S,x:S),z:S,u:S),f(x:S,u:S,z:S,u:S)) perfectp(0) -> ffalse perfectp(s(x:S)) -> f(x:S,s(0),s(x:S),s(x:S)) Problem 1: Subterm Processor: -> Pairs: F(s(x:S),0,z:S,u:S) -> F(x:S,u:S,minus(z:S,s(x:S)),u:S) F(s(x:S),s(y:S),z:S,u:S) -> F(x:S,u:S,z:S,u:S) -> Rules: f(0,y:S,0,u:S) -> ttrue f(0,y:S,s(z:S),u:S) -> ffalse f(s(x:S),0,z:S,u:S) -> f(x:S,u:S,minus(z:S,s(x:S)),u:S) f(s(x:S),s(y:S),z:S,u:S) -> if(le(x:S,y:S),f(s(x:S),minus(y:S,x:S),z:S,u:S),f(x:S,u:S,z:S,u:S)) perfectp(0) -> ffalse perfectp(s(x:S)) -> f(x:S,s(0),s(x:S),s(x:S)) ->Projection: pi(F) = 1 Problem 1: SCC Processor: -> Pairs: Empty -> Rules: f(0,y:S,0,u:S) -> ttrue f(0,y:S,s(z:S),u:S) -> ffalse f(s(x:S),0,z:S,u:S) -> f(x:S,u:S,minus(z:S,s(x:S)),u:S) f(s(x:S),s(y:S),z:S,u:S) -> if(le(x:S,y:S),f(s(x:S),minus(y:S,x:S),z:S,u:S),f(x:S,u:S,z:S,u:S)) perfectp(0) -> ffalse perfectp(s(x:S)) -> f(x:S,s(0),s(x:S),s(x:S)) ->Strongly Connected Components: There is no strongly connected component popout

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