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TRS Standard pair #487072624
details
property
value
status
complete
benchmark
23.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n175.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.181511 seconds
cpu usage
0.15507
user time
0.088081
system time
0.066989
max virtual memory
113188.0
max residence set size
5812.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S y:S z:S) (RULES cond1(ttrue,x:S,y:S,z:S) -> cond2(gr(y:S,z:S),x:S,y:S,z:S) cond2(ffalse,x:S,y:S,z:S) -> cond1(gr(x:S,z:S),p(x:S),y:S,z:S) cond2(ttrue,x:S,y:S,z:S) -> cond2(gr(y:S,z:S),x:S,p(y:S),z: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,z:S) -> cond2(gr(y:S,z:S),x:S,y:S,z:S) cond2(ffalse,x:S,y:S,z:S) -> cond1(gr(x:S,z:S),p(x:S),y:S,z:S) cond2(ttrue,x:S,y:S,z:S) -> cond2(gr(y:S,z:S),x:S,p(y:S),z: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,z:S) -> COND2(gr(y:S,z:S),x:S,y:S,z:S) COND1(ttrue,x:S,y:S,z:S) -> GR(y:S,z:S) COND2(ffalse,x:S,y:S,z:S) -> COND1(gr(x:S,z:S),p(x:S),y:S,z:S) COND2(ffalse,x:S,y:S,z:S) -> GR(x:S,z:S) COND2(ffalse,x:S,y:S,z:S) -> P(x:S) COND2(ttrue,x:S,y:S,z:S) -> COND2(gr(y:S,z:S),x:S,p(y:S),z:S) COND2(ttrue,x:S,y:S,z:S) -> GR(y:S,z:S) COND2(ttrue,x:S,y:S,z:S) -> P(y:S) GR(s(x:S),s(y:S)) -> GR(x:S,y:S) -> Rules: cond1(ttrue,x:S,y:S,z:S) -> cond2(gr(y:S,z:S),x:S,y:S,z:S) cond2(ffalse,x:S,y:S,z:S) -> cond1(gr(x:S,z:S),p(x:S),y:S,z:S) cond2(ttrue,x:S,y:S,z:S) -> cond2(gr(y:S,z:S),x:S,p(y:S),z: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,z:S) -> COND2(gr(y:S,z:S),x:S,y:S,z:S) COND1(ttrue,x:S,y:S,z:S) -> GR(y:S,z:S) COND2(ffalse,x:S,y:S,z:S) -> COND1(gr(x:S,z:S),p(x:S),y:S,z:S) COND2(ffalse,x:S,y:S,z:S) -> GR(x:S,z:S) COND2(ffalse,x:S,y:S,z:S) -> P(x:S) COND2(ttrue,x:S,y:S,z:S) -> COND2(gr(y:S,z:S),x:S,p(y:S),z:S) COND2(ttrue,x:S,y:S,z:S) -> GR(y:S,z:S) COND2(ttrue,x:S,y:S,z:S) -> P(y:S) GR(s(x:S),s(y:S)) -> GR(x:S,y:S) -> Rules: cond1(ttrue,x:S,y:S,z:S) -> cond2(gr(y:S,z:S),x:S,y:S,z:S) cond2(ffalse,x:S,y:S,z:S) -> cond1(gr(x:S,z:S),p(x:S),y:S,z:S) cond2(ttrue,x:S,y:S,z:S) -> cond2(gr(y:S,z:S),x:S,p(y:S),z: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,z:S) -> cond2(gr(y:S,z:S),x:S,y:S,z:S) cond2(ffalse,x:S,y:S,z:S) -> cond1(gr(x:S,z:S),p(x:S),y:S,z:S) cond2(ttrue,x:S,y:S,z:S) -> cond2(gr(y:S,z:S),x:S,p(y:S),z: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,z:S) -> COND2(gr(y:S,z:S),x:S,y:S,z:S) COND2(ffalse,x:S,y:S,z:S) -> COND1(gr(x:S,z:S),p(x:S),y:S,z:S) COND2(ttrue,x:S,y:S,z:S) -> COND2(gr(y:S,z:S),x:S,p(y:S),z:S) ->->-> Rules: cond1(ttrue,x:S,y:S,z:S) -> cond2(gr(y:S,z:S),x:S,y:S,z:S) cond2(ffalse,x:S,y:S,z:S) -> cond1(gr(x:S,z:S),p(x:S),y:S,z:S) cond2(ttrue,x:S,y:S,z:S) -> cond2(gr(y:S,z:S),x:S,p(y:S),z:S) gr(0,x:S) -> ffalse gr(s(x:S),0) -> ttrue
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