details

property	value
status	complete
benchmark	5.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n070.star.cs.uiowa.edu
space	Beerendonk_07

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.104357 seconds
cpu usage	0.093876
user time	0.063566
system time	0.03031
max virtual memory	113188.0
max residence set size	5576.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S x:S) (RULES and(ffalse,x:S) -> ffalse and(ttrue,ttrue) -> ttrue and(x:S,ffalse) -> ffalse cond(ttrue,x:S) -> cond(and(even(x:S),gr(x:S,0)),p(x:S)) even(0) -> ttrue even(s(0)) -> ffalse even(s(s(x:S))) -> even(x:S) gr(0,x:S) -> ffalse gr(s(x:S),0) -> ttrue gr(s(x:S),s(y)) -> gr(x:S,y) p(0) -> 0 p(s(x:S)) -> x:S ) Problem 1: Innermost Equivalent Processor: -> Rules: and(ffalse,x:S) -> ffalse and(ttrue,ttrue) -> ttrue and(x:S,ffalse) -> ffalse cond(ttrue,x:S) -> cond(and(even(x:S),gr(x:S,0)),p(x:S)) even(0) -> ttrue even(s(0)) -> ffalse even(s(s(x:S))) -> even(x:S) gr(0,x:S) -> ffalse gr(s(x:S),0) -> ttrue gr(s(x:S),s(y)) -> gr(x:S,y) 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: COND(ttrue,x:S) -> AND(even(x:S),gr(x:S,0)) COND(ttrue,x:S) -> COND(and(even(x:S),gr(x:S,0)),p(x:S)) COND(ttrue,x:S) -> EVEN(x:S) COND(ttrue,x:S) -> GR(x:S,0) COND(ttrue,x:S) -> P(x:S) EVEN(s(s(x:S))) -> EVEN(x:S) GR(s(x:S),s(y)) -> GR(x:S,y) -> Rules: and(ffalse,x:S) -> ffalse and(ttrue,ttrue) -> ttrue and(x:S,ffalse) -> ffalse cond(ttrue,x:S) -> cond(and(even(x:S),gr(x:S,0)),p(x:S)) even(0) -> ttrue even(s(0)) -> ffalse even(s(s(x:S))) -> even(x:S) gr(0,x:S) -> ffalse gr(s(x:S),0) -> ttrue gr(s(x:S),s(y)) -> gr(x:S,y) p(0) -> 0 p(s(x:S)) -> x:S Problem 1: SCC Processor: -> Pairs: COND(ttrue,x:S) -> AND(even(x:S),gr(x:S,0)) COND(ttrue,x:S) -> COND(and(even(x:S),gr(x:S,0)),p(x:S)) COND(ttrue,x:S) -> EVEN(x:S) COND(ttrue,x:S) -> GR(x:S,0) COND(ttrue,x:S) -> P(x:S) EVEN(s(s(x:S))) -> EVEN(x:S) GR(s(x:S),s(y)) -> GR(x:S,y) -> Rules: and(ffalse,x:S) -> ffalse and(ttrue,ttrue) -> ttrue and(x:S,ffalse) -> ffalse cond(ttrue,x:S) -> cond(and(even(x:S),gr(x:S,0)),p(x:S)) even(0) -> ttrue even(s(0)) -> ffalse even(s(s(x:S))) -> even(x:S) gr(0,x:S) -> ffalse gr(s(x:S),0) -> ttrue gr(s(x:S),s(y)) -> gr(x:S,y) p(0) -> 0 p(s(x:S)) -> x:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: EVEN(s(s(x:S))) -> EVEN(x:S) ->->-> Rules: and(ffalse,x:S) -> ffalse and(ttrue,ttrue) -> ttrue and(x:S,ffalse) -> ffalse cond(ttrue,x:S) -> cond(and(even(x:S),gr(x:S,0)),p(x:S)) even(0) -> ttrue even(s(0)) -> ffalse even(s(s(x:S))) -> even(x:S) popout

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