details

property	value
status	complete
benchmark	22.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n173.star.cs.uiowa.edu
space	Beerendonk_07

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.166828 seconds
cpu usage	0.154312
user time	0.07791
system time	0.076402
max virtual memory	113188.0
max residence set size	5764.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES cond1(ttrue,x:S,y:S) -> cond2(gr(y:S,0),x:S,y:S) cond2(ffalse,x:S,y:S) -> cond1(gr(x:S,0),p(x:S),y:S) cond2(ttrue,x:S,y:S) -> cond2(gr(y:S,0),x:S,p(y:S)) gr(0,x:S) -> ffalse gr(s(x:S),0) -> ttrue gr(s(x:S),s(y:S)) -> gr(x:S,y:S) p(0) -> 0 p(s(x:S)) -> x:S ) Problem 1: Innermost Equivalent Processor: -> Rules: cond1(ttrue,x:S,y:S) -> cond2(gr(y:S,0),x:S,y:S) cond2(ffalse,x:S,y:S) -> cond1(gr(x:S,0),p(x:S),y:S) cond2(ttrue,x:S,y:S) -> cond2(gr(y:S,0),x:S,p(y:S)) gr(0,x:S) -> ffalse gr(s(x:S),0) -> ttrue gr(s(x:S),s(y:S)) -> gr(x:S,y:S) p(0) -> 0 p(s(x: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: COND1(ttrue,x:S,y:S) -> COND2(gr(y:S,0),x:S,y:S) COND1(ttrue,x:S,y:S) -> GR(y:S,0) COND2(ffalse,x:S,y:S) -> COND1(gr(x:S,0),p(x:S),y:S) COND2(ffalse,x:S,y:S) -> GR(x:S,0) COND2(ffalse,x:S,y:S) -> P(x:S) COND2(ttrue,x:S,y:S) -> COND2(gr(y:S,0),x:S,p(y:S)) COND2(ttrue,x:S,y:S) -> GR(y:S,0) COND2(ttrue,x:S,y:S) -> P(y:S) GR(s(x:S),s(y:S)) -> GR(x:S,y:S) -> Rules: cond1(ttrue,x:S,y:S) -> cond2(gr(y:S,0),x:S,y:S) cond2(ffalse,x:S,y:S) -> cond1(gr(x:S,0),p(x:S),y:S) cond2(ttrue,x:S,y:S) -> cond2(gr(y:S,0),x:S,p(y:S)) gr(0,x:S) -> ffalse gr(s(x:S),0) -> ttrue gr(s(x:S),s(y:S)) -> gr(x:S,y:S) p(0) -> 0 p(s(x:S)) -> x:S Problem 1: SCC Processor: -> Pairs: COND1(ttrue,x:S,y:S) -> COND2(gr(y:S,0),x:S,y:S) COND1(ttrue,x:S,y:S) -> GR(y:S,0) COND2(ffalse,x:S,y:S) -> COND1(gr(x:S,0),p(x:S),y:S) COND2(ffalse,x:S,y:S) -> GR(x:S,0) COND2(ffalse,x:S,y:S) -> P(x:S) COND2(ttrue,x:S,y:S) -> COND2(gr(y:S,0),x:S,p(y:S)) COND2(ttrue,x:S,y:S) -> GR(y:S,0) COND2(ttrue,x:S,y:S) -> P(y:S) GR(s(x:S),s(y:S)) -> GR(x:S,y:S) -> Rules: cond1(ttrue,x:S,y:S) -> cond2(gr(y:S,0),x:S,y:S) cond2(ffalse,x:S,y:S) -> cond1(gr(x:S,0),p(x:S),y:S) cond2(ttrue,x:S,y:S) -> cond2(gr(y:S,0),x:S,p(y:S)) gr(0,x:S) -> ffalse gr(s(x:S),0) -> ttrue gr(s(x:S),s(y:S)) -> gr(x:S,y:S) p(0) -> 0 p(s(x:S)) -> x:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: GR(s(x:S),s(y:S)) -> GR(x:S,y:S) ->->-> Rules: cond1(ttrue,x:S,y:S) -> cond2(gr(y:S,0),x:S,y:S) cond2(ffalse,x:S,y:S) -> cond1(gr(x:S,0),p(x:S),y:S) cond2(ttrue,x:S,y:S) -> cond2(gr(y:S,0),x:S,p(y:S)) gr(0,x:S) -> ffalse gr(s(x:S),0) -> ttrue gr(s(x:S),s(y:S)) -> gr(x:S,y:S) p(0) -> 0 p(s(x:S)) -> x:S ->->Cycle: ->->-> Pairs: COND1(ttrue,x:S,y:S) -> COND2(gr(y:S,0),x:S,y:S) COND2(ffalse,x:S,y:S) -> COND1(gr(x:S,0),p(x:S),y:S) COND2(ttrue,x:S,y:S) -> COND2(gr(y:S,0),x:S,p(y:S)) ->->-> Rules: cond1(ttrue,x:S,y:S) -> cond2(gr(y:S,0),x:S,y:S) cond2(ffalse,x:S,y:S) -> cond1(gr(x:S,0),p(x:S),y:S) cond2(ttrue,x:S,y:S) -> cond2(gr(y:S,0),x:S,p(y:S)) gr(0,x:S) -> ffalse gr(s(x:S),0) -> ttrue popout

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