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TRS Standard pair #516960701
details
property
value
status
complete
benchmark
thiemann12.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n174.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.240510940552 seconds
cpu usage
0.113419008
max memory
4423680.0
stage attributes
key
value
output-size
8599
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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)) if(ffalse,x:S,y:S) -> log2(half(x:S),y:S) if(ttrue,x:S,s(y:S)) -> y:S inc(0) -> 0 inc(s(x:S)) -> s(inc(x:S)) le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) log(x:S) -> log2(x:S,0) log2(x:S,y:S) -> if(le(x:S,s(0)),x:S,inc(y:S)) ) Problem 1: Innermost Equivalent Processor: -> Rules: half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) if(ffalse,x:S,y:S) -> log2(half(x:S),y:S) if(ttrue,x:S,s(y:S)) -> y:S inc(0) -> 0 inc(s(x:S)) -> s(inc(x:S)) le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) log(x:S) -> log2(x:S,0) log2(x:S,y:S) -> if(le(x:S,s(0)),x:S,inc(y:S)) -> 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) IF(ffalse,x:S,y:S) -> HALF(x:S) IF(ffalse,x:S,y:S) -> LOG2(half(x:S),y:S) INC(s(x:S)) -> INC(x:S) LE(s(x:S),s(y:S)) -> LE(x:S,y:S) LOG(x:S) -> LOG2(x:S,0) LOG2(x:S,y:S) -> IF(le(x:S,s(0)),x:S,inc(y:S)) LOG2(x:S,y:S) -> INC(y:S) LOG2(x:S,y:S) -> LE(x:S,s(0)) -> Rules: half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) if(ffalse,x:S,y:S) -> log2(half(x:S),y:S) if(ttrue,x:S,s(y:S)) -> y:S inc(0) -> 0 inc(s(x:S)) -> s(inc(x:S)) le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) log(x:S) -> log2(x:S,0) log2(x:S,y:S) -> if(le(x:S,s(0)),x:S,inc(y:S)) Problem 1: SCC Processor: -> Pairs: HALF(s(s(x:S))) -> HALF(x:S) IF(ffalse,x:S,y:S) -> HALF(x:S) IF(ffalse,x:S,y:S) -> LOG2(half(x:S),y:S) INC(s(x:S)) -> INC(x:S) LE(s(x:S),s(y:S)) -> LE(x:S,y:S) LOG(x:S) -> LOG2(x:S,0) LOG2(x:S,y:S) -> IF(le(x:S,s(0)),x:S,inc(y:S)) LOG2(x:S,y:S) -> INC(y:S) LOG2(x:S,y:S) -> LE(x:S,s(0)) -> Rules: half(0) -> 0 half(s(0)) -> 0 half(s(s(x:S))) -> s(half(x:S)) if(ffalse,x:S,y:S) -> log2(half(x:S),y:S) if(ttrue,x:S,s(y:S)) -> y:S inc(0) -> 0 inc(s(x:S)) -> s(inc(x:S)) le(0,y:S) -> ttrue le(s(x:S),0) -> ffalse le(s(x:S),s(y:S)) -> le(x:S,y:S) log(x:S) -> log2(x:S,0) log2(x:S,y:S) -> if(le(x:S,s(0)),x:S,inc(y:S)) ->Strongly Connected Components: ->->Cycle:
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