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TRS Standard pair #516968096
details
property
value
status
complete
benchmark
t014.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n009.star.cs.uiowa.edu
space
HirokawaMiddeldorp_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0814900398254 seconds
cpu usage
0.041579119
max memory
3342336.0
stage attributes
key
value
output-size
6500
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 -(0,s(y:S)) -> 0 -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S div(0,y:S) -> 0 div(s(x:S),s(y:S)) -> if(lt(x:S,y:S),0,s(div(-(x:S,y:S),s(y:S)))) div(x:S,0) -> 0 if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S lt(0,s(y: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: -(0,s(y:S)) -> 0 -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S div(0,y:S) -> 0 div(s(x:S),s(y:S)) -> if(lt(x:S,y:S),0,s(div(-(x:S,y:S),s(y:S)))) div(x:S,0) -> 0 if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S lt(0,s(y: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: -#(s(x:S),s(y:S)) -> -#(x:S,y:S) DIV(s(x:S),s(y:S)) -> -#(x:S,y:S) DIV(s(x:S),s(y:S)) -> DIV(-(x:S,y:S),s(y:S)) DIV(s(x:S),s(y:S)) -> IF(lt(x:S,y:S),0,s(div(-(x:S,y:S),s(y:S)))) DIV(s(x:S),s(y:S)) -> LT(x:S,y:S) LT(s(x:S),s(y:S)) -> LT(x:S,y:S) -> Rules: -(0,s(y:S)) -> 0 -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S div(0,y:S) -> 0 div(s(x:S),s(y:S)) -> if(lt(x:S,y:S),0,s(div(-(x:S,y:S),s(y:S)))) div(x:S,0) -> 0 if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S lt(0,s(y:S)) -> ttrue lt(s(x:S),s(y:S)) -> lt(x:S,y:S) lt(x:S,0) -> ffalse Problem 1: SCC Processor: -> Pairs: -#(s(x:S),s(y:S)) -> -#(x:S,y:S) DIV(s(x:S),s(y:S)) -> -#(x:S,y:S) DIV(s(x:S),s(y:S)) -> DIV(-(x:S,y:S),s(y:S)) DIV(s(x:S),s(y:S)) -> IF(lt(x:S,y:S),0,s(div(-(x:S,y:S),s(y:S)))) DIV(s(x:S),s(y:S)) -> LT(x:S,y:S) LT(s(x:S),s(y:S)) -> LT(x:S,y:S) -> Rules: -(0,s(y:S)) -> 0 -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S div(0,y:S) -> 0 div(s(x:S),s(y:S)) -> if(lt(x:S,y:S),0,s(div(-(x:S,y:S),s(y:S)))) div(x:S,0) -> 0 if(ffalse,x:S,y:S) -> y:S if(ttrue,x:S,y:S) -> x:S lt(0,s(y: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: -(0,s(y:S)) -> 0 -(s(x:S),s(y:S)) -> -(x:S,y:S) -(x:S,0) -> x:S div(0,y:S) -> 0 div(s(x:S),s(y:S)) -> if(lt(x:S,y:S),0,s(div(-(x:S,y:S),s(y:S)))) div(x:S,0) -> 0 if(ffalse,x:S,y:S) -> y:S
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