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TRS Standard pair #487072644
details
property
value
status
complete
benchmark
8.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n180.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.118888 seconds
cpu usage
0.085237
user time
0.048944
system time
0.036293
max virtual memory
113188.0
max residence set size
5580.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES and(ffalse,x:S) -> ffalse and(ttrue,ttrue) -> ttrue and(x:S,ffalse) -> ffalse cond(ttrue,x:S,y:S) -> cond(and(gr(x:S,0),gr(y:S,0)),p(x:S),p(y:S)) gr(0,0) -> ffalse 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: and(ffalse,x:S) -> ffalse and(ttrue,ttrue) -> ttrue and(x:S,ffalse) -> ffalse cond(ttrue,x:S,y:S) -> cond(and(gr(x:S,0),gr(y:S,0)),p(x:S),p(y:S)) gr(0,0) -> ffalse 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: COND(ttrue,x:S,y:S) -> AND(gr(x:S,0),gr(y:S,0)) COND(ttrue,x:S,y:S) -> COND(and(gr(x:S,0),gr(y:S,0)),p(x:S),p(y:S)) COND(ttrue,x:S,y:S) -> GR(x:S,0) COND(ttrue,x:S,y:S) -> GR(y:S,0) COND(ttrue,x:S,y:S) -> P(x:S) COND(ttrue,x:S,y:S) -> P(y:S) GR(s(x:S),s(y:S)) -> GR(x:S,y:S) -> Rules: and(ffalse,x:S) -> ffalse and(ttrue,ttrue) -> ttrue and(x:S,ffalse) -> ffalse cond(ttrue,x:S,y:S) -> cond(and(gr(x:S,0),gr(y:S,0)),p(x:S),p(y:S)) gr(0,0) -> ffalse 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: COND(ttrue,x:S,y:S) -> AND(gr(x:S,0),gr(y:S,0)) COND(ttrue,x:S,y:S) -> COND(and(gr(x:S,0),gr(y:S,0)),p(x:S),p(y:S)) COND(ttrue,x:S,y:S) -> GR(x:S,0) COND(ttrue,x:S,y:S) -> GR(y:S,0) COND(ttrue,x:S,y:S) -> P(x:S) COND(ttrue,x:S,y:S) -> P(y:S) GR(s(x:S),s(y:S)) -> GR(x:S,y:S) -> Rules: and(ffalse,x:S) -> ffalse and(ttrue,ttrue) -> ttrue and(x:S,ffalse) -> ffalse cond(ttrue,x:S,y:S) -> cond(and(gr(x:S,0),gr(y:S,0)),p(x:S),p(y:S)) gr(0,0) -> ffalse 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: and(ffalse,x:S) -> ffalse and(ttrue,ttrue) -> ttrue and(x:S,ffalse) -> ffalse cond(ttrue,x:S,y:S) -> cond(and(gr(x:S,0),gr(y:S,0)),p(x:S),p(y:S)) gr(0,0) -> ffalse 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: COND(ttrue,x:S,y:S) -> COND(and(gr(x:S,0),gr(y:S,0)),p(x:S),p(y:S)) ->->-> Rules: and(ffalse,x:S) -> ffalse
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