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TRS Standard pair #516964206
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
n065.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.152306079865 seconds
cpu usage
0.096712007
max memory
4407296.0
stage attributes
key
value
output-size
5645
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- 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
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