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TRS Standard pair #487067469
details
property
value
status
complete
benchmark
#3.37.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n178.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0180261 seconds
cpu usage
0.018419
user time
0.006938
system time
0.011481
max virtual memory
113188.0
max residence set size
4316.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S) (RULES evenodd(0,s(0)) -> ffalse evenodd(s(x:S),s(0)) -> evenodd(x:S,0) evenodd(x:S,0) -> not(evenodd(x:S,s(0))) not(ffalse) -> ttrue not(ttrue) -> ffalse ) Problem 1: Innermost Equivalent Processor: -> Rules: evenodd(0,s(0)) -> ffalse evenodd(s(x:S),s(0)) -> evenodd(x:S,0) evenodd(x:S,0) -> not(evenodd(x:S,s(0))) not(ffalse) -> ttrue not(ttrue) -> ffalse -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: EVENODD(s(x:S),s(0)) -> EVENODD(x:S,0) EVENODD(x:S,0) -> EVENODD(x:S,s(0)) EVENODD(x:S,0) -> NOT(evenodd(x:S,s(0))) -> Rules: evenodd(0,s(0)) -> ffalse evenodd(s(x:S),s(0)) -> evenodd(x:S,0) evenodd(x:S,0) -> not(evenodd(x:S,s(0))) not(ffalse) -> ttrue not(ttrue) -> ffalse Problem 1: SCC Processor: -> Pairs: EVENODD(s(x:S),s(0)) -> EVENODD(x:S,0) EVENODD(x:S,0) -> EVENODD(x:S,s(0)) EVENODD(x:S,0) -> NOT(evenodd(x:S,s(0))) -> Rules: evenodd(0,s(0)) -> ffalse evenodd(s(x:S),s(0)) -> evenodd(x:S,0) evenodd(x:S,0) -> not(evenodd(x:S,s(0))) not(ffalse) -> ttrue not(ttrue) -> ffalse ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: EVENODD(s(x:S),s(0)) -> EVENODD(x:S,0) EVENODD(x:S,0) -> EVENODD(x:S,s(0)) ->->-> Rules: evenodd(0,s(0)) -> ffalse evenodd(s(x:S),s(0)) -> evenodd(x:S,0) evenodd(x:S,0) -> not(evenodd(x:S,s(0))) not(ffalse) -> ttrue not(ttrue) -> ffalse Problem 1: Subterm Processor: -> Pairs: EVENODD(s(x:S),s(0)) -> EVENODD(x:S,0) EVENODD(x:S,0) -> EVENODD(x:S,s(0)) -> Rules: evenodd(0,s(0)) -> ffalse evenodd(s(x:S),s(0)) -> evenodd(x:S,0) evenodd(x:S,0) -> not(evenodd(x:S,s(0))) not(ffalse) -> ttrue not(ttrue) -> ffalse ->Projection: pi(EVENODD) = 1 Problem 1: SCC Processor: -> Pairs: EVENODD(x:S,0) -> EVENODD(x:S,s(0)) -> Rules: evenodd(0,s(0)) -> ffalse evenodd(s(x:S),s(0)) -> evenodd(x:S,0) evenodd(x:S,0) -> not(evenodd(x:S,s(0))) not(ffalse) -> ttrue not(ttrue) -> ffalse ->Strongly Connected Components: There is no strongly connected component The problem is finite.
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