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TRS Standard pair #487073264
details
property
value
status
complete
benchmark
otto05.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n189.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.1081 seconds
cpu usage
0.089556
user time
0.049519
system time
0.040037
max virtual memory
113188.0
max residence set size
5760.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) help(x:S,y:S) -> ifb(lt(y:S,x:S),x:S,y:S) ifa(ffalse,x:S) -> logZeroError ifa(ttrue,x:S) -> help(x:S,1) ifb(ffalse,x:S,y:S) -> y:S ifb(ttrue,x:S,y:S) -> help(half(x:S),s(y:S)) logarithm(x:S) -> ifa(lt(0,x:S),x:S) lt(0,s(x:S)) -> ttrue lt(s(x:S),s(y:S)) -> lt(x:S,y:S) lt(x:S,0) -> ffalse ) Problem 1: Innermost Equivalent Processor: -> Rules: half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) help(x:S,y:S) -> ifb(lt(y:S,x:S),x:S,y:S) ifa(ffalse,x:S) -> logZeroError ifa(ttrue,x:S) -> help(x:S,1) ifb(ffalse,x:S,y:S) -> y:S ifb(ttrue,x:S,y:S) -> help(half(x:S),s(y:S)) logarithm(x:S) -> ifa(lt(0,x:S),x:S) lt(0,s(x:S)) -> ttrue lt(s(x:S),s(y:S)) -> lt(x:S,y:S) lt(x:S,0) -> ffalse -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: HALF(s(s(x:S))) -> HALF(x:S) HELP(x:S,y:S) -> IFB(lt(y:S,x:S),x:S,y:S) HELP(x:S,y:S) -> LT(y:S,x:S) IFA(ttrue,x:S) -> HELP(x:S,1) IFB(ttrue,x:S,y:S) -> HALF(x:S) IFB(ttrue,x:S,y:S) -> HELP(half(x:S),s(y:S)) LOGARITHM(x:S) -> IFA(lt(0,x:S),x:S) LOGARITHM(x:S) -> LT(0,x:S) LT(s(x:S),s(y:S)) -> LT(x:S,y:S) -> Rules: half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) help(x:S,y:S) -> ifb(lt(y:S,x:S),x:S,y:S) ifa(ffalse,x:S) -> logZeroError ifa(ttrue,x:S) -> help(x:S,1) ifb(ffalse,x:S,y:S) -> y:S ifb(ttrue,x:S,y:S) -> help(half(x:S),s(y:S)) logarithm(x:S) -> ifa(lt(0,x:S),x:S) lt(0,s(x:S)) -> ttrue lt(s(x:S),s(y:S)) -> lt(x:S,y:S) lt(x:S,0) -> ffalse Problem 1: SCC Processor: -> Pairs: HALF(s(s(x:S))) -> HALF(x:S) HELP(x:S,y:S) -> IFB(lt(y:S,x:S),x:S,y:S) HELP(x:S,y:S) -> LT(y:S,x:S) IFA(ttrue,x:S) -> HELP(x:S,1) IFB(ttrue,x:S,y:S) -> HALF(x:S) IFB(ttrue,x:S,y:S) -> HELP(half(x:S),s(y:S)) LOGARITHM(x:S) -> IFA(lt(0,x:S),x:S) LOGARITHM(x:S) -> LT(0,x:S) LT(s(x:S),s(y:S)) -> LT(x:S,y:S) -> Rules: half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) help(x:S,y:S) -> ifb(lt(y:S,x:S),x:S,y:S) ifa(ffalse,x:S) -> logZeroError ifa(ttrue,x:S) -> help(x:S,1) ifb(ffalse,x:S,y:S) -> y:S ifb(ttrue,x:S,y:S) -> help(half(x:S),s(y:S)) logarithm(x:S) -> ifa(lt(0,x:S),x:S) lt(0,s(x:S)) -> ttrue lt(s(x:S),s(y:S)) -> lt(x:S,y:S) lt(x:S,0) -> ffalse ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: LT(s(x:S),s(y:S)) -> LT(x:S,y:S) ->->-> Rules: half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S))
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