details

property	value
status	complete
benchmark	4.12.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n094.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.10474896431 seconds
cpu usage	0.039991034
max memory	3252224.0

stage attributes

key	value
output-size	1996
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,y:S) -> y:S +(s(x:S),0) -> s(x:S) +(s(x:S),s(y:S)) -> s(+(s(x:S),+(y:S,0))) ) Problem 1: Innermost Equivalent Processor: -> Rules: +(0,y:S) -> y:S +(s(x:S),0) -> s(x:S) +(s(x:S),s(y:S)) -> s(+(s(x:S),+(y:S,0))) -> 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)) -> +#(s(x:S),+(y:S,0)) +#(s(x:S),s(y:S)) -> +#(y:S,0) -> Rules: +(0,y:S) -> y:S +(s(x:S),0) -> s(x:S) +(s(x:S),s(y:S)) -> s(+(s(x:S),+(y:S,0))) Problem 1: SCC Processor: -> Pairs: +#(s(x:S),s(y:S)) -> +#(s(x:S),+(y:S,0)) +#(s(x:S),s(y:S)) -> +#(y:S,0) -> Rules: +(0,y:S) -> y:S +(s(x:S),0) -> s(x:S) +(s(x:S),s(y:S)) -> s(+(s(x:S),+(y:S,0))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: +#(s(x:S),s(y:S)) -> +#(s(x:S),+(y:S,0)) ->->-> Rules: +(0,y:S) -> y:S +(s(x:S),0) -> s(x:S) +(s(x:S),s(y:S)) -> s(+(s(x:S),+(y:S,0))) Problem 1: Reduction Pairs Processor: -> Pairs: +#(s(x:S),s(y:S)) -> +#(s(x:S),+(y:S,0)) -> Rules: +(0,y:S) -> y:S +(s(x:S),0) -> s(x:S) +(s(x:S),s(y:S)) -> s(+(s(x:S),+(y:S,0))) -> Usable rules: +(0,y:S) -> y:S +(s(x:S),0) -> s(x:S) +(s(x:S),s(y:S)) -> s(+(s(x:S),+(y:S,0))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [+](X1,X2) = X1 + 2.X2 + 1 [0] = 0 [fSNonEmpty] = 0 [s](X) = X + 2 [+#](X1,X2) = 2.X2 Problem 1: SCC Processor: -> Pairs: Empty -> Rules: +(0,y:S) -> y:S +(s(x:S),0) -> s(x:S) +(s(x:S),s(y:S)) -> s(+(s(x:S),+(y:S,0))) ->Strongly Connected Components: There is no strongly connected component The problem is finite. popout

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