details

property	value
status	complete
benchmark	jw27.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n175.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.141399 seconds
cpu usage	0.118228
user time	0.088404
system time	0.029824
max virtual memory	113188.0
max residence set size	5436.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S x:S) (RULES f(f(a,x:S),a) -> f(a,f(f(x:S,f(a,a)),a)) ) Problem 1: Innermost Equivalent Processor: -> Rules: f(f(a,x:S),a) -> f(a,f(f(x:S,f(a,a)),a)) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: F(f(a,x:S),a) -> F(f(x:S,f(a,a)),a) F(f(a,x:S),a) -> F(a,f(f(x:S,f(a,a)),a)) -> Rules: f(f(a,x:S),a) -> f(a,f(f(x:S,f(a,a)),a)) Problem 1: SCC Processor: -> Pairs: F(f(a,x:S),a) -> F(f(x:S,f(a,a)),a) F(f(a,x:S),a) -> F(a,f(f(x:S,f(a,a)),a)) -> Rules: f(f(a,x:S),a) -> f(a,f(f(x:S,f(a,a)),a)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(f(a,x:S),a) -> F(f(x:S,f(a,a)),a) ->->-> Rules: f(f(a,x:S),a) -> f(a,f(f(x:S,f(a,a)),a)) Problem 1: Reduction Pairs Processor: -> Pairs: F(f(a,x:S),a) -> F(f(x:S,f(a,a)),a) -> Rules: f(f(a,x:S),a) -> f(a,f(f(x:S,f(a,a)),a)) -> Usable rules: f(f(a,x:S),a) -> f(a,f(f(x:S,f(a,a)),a)) ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 4 ->Interpretation: [f](X1,X2) = 1/4.X1 + 1/3.X2 + 1/3 [a] = 4 [fSNonEmpty] = 0 [F](X1,X2) = 4.X1 Problem 1: SCC Processor: -> Pairs: Empty -> Rules: f(f(a,x:S),a) -> f(a,f(f(x:S,f(a,a)),a)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. popout

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