details

property	value
status	complete
benchmark	perfect2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n181.star.cs.uiowa.edu
space	Mixed_TRS

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.0587459 seconds
cpu usage	0.046927
user time	0.019447
system time	0.02748
max virtual memory	113188.0
max residence set size	6108.0

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)) if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) minus(0,y:S) -> 0 minus(s(x:S),0) -> s(x:S) minus(s(x:S),s(y:S)) -> minus(x:S,y: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)) if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) minus(0,y:S) -> 0 minus(s(x:S),0) -> s(x:S) minus(s(x:S),s(y:S)) -> minus(x:S,y: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),0,z:S,u:S) -> MINUS(z:S,s(x:S)) F(s(x:S),s(y:S),z:S,u:S) -> F(s(x:S),minus(y:S,x:S),z:S,u:S) F(s(x:S),s(y:S),z:S,u:S) -> F(x:S,u:S,z: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)) F(s(x:S),s(y:S),z:S,u:S) -> LE(x:S,y:S) F(s(x:S),s(y:S),z:S,u:S) -> MINUS(y:S,x:S) LE(s(x:S),s(y:S)) -> LE(x:S,y:S) MINUS(s(x:S),s(y:S)) -> MINUS(x:S,y: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)) if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) minus(0,y:S) -> 0 minus(s(x:S),0) -> s(x:S) minus(s(x:S),s(y:S)) -> minus(x:S,y: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),0,z:S,u:S) -> MINUS(z:S,s(x:S)) F(s(x:S),s(y:S),z:S,u:S) -> F(s(x:S),minus(y:S,x:S),z:S,u:S) F(s(x:S),s(y:S),z:S,u:S) -> F(x:S,u:S,z: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)) F(s(x:S),s(y:S),z:S,u:S) -> LE(x:S,y:S) F(s(x:S),s(y:S),z:S,u:S) -> MINUS(y:S,x:S) LE(s(x:S),s(y:S)) -> LE(x:S,y:S) MINUS(s(x:S),s(y:S)) -> MINUS(x:S,y: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)) if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) minus(0,y:S) -> 0 minus(s(x:S),0) -> s(x:S) minus(s(x:S),s(y:S)) -> minus(x:S,y:S) popout

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actions

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