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TRS Standard pair #516960936
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
n137.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.2345058918 seconds
cpu usage
0.094775033
max memory
4186112.0
stage attributes
key
value
output-size
7751
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 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:
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