details

property	value
status	complete
benchmark	jw18.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n173.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.381809 seconds
cpu usage	0.352874
user time	0.287008
system time	0.065866
max virtual memory	113188.0
max residence set size	5508.0

stage attributes

key	value
starexec-result	YES

output

YES Problem 1: (VAR v_NonEmpty:S x:S) (RULES f(x:S,f(a,a)) -> f(f(f(a,a),a),f(x:S,a)) ) Problem 1: Innermost Equivalent Processor: -> Rules: f(x:S,f(a,a)) -> f(f(f(a,a),a),f(x:S,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(x:S,f(a,a)) -> F(f(f(a,a),a),f(x:S,a)) -> Rules: f(x:S,f(a,a)) -> f(f(f(a,a),a),f(x:S,a)) Problem 1: SCC Processor: -> Pairs: F(x:S,f(a,a)) -> F(f(f(a,a),a),f(x:S,a)) -> Rules: f(x:S,f(a,a)) -> f(f(f(a,a),a),f(x:S,a)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(x:S,f(a,a)) -> F(f(f(a,a),a),f(x:S,a)) ->->-> Rules: f(x:S,f(a,a)) -> f(f(f(a,a),a),f(x:S,a)) Problem 1: Reduction Pairs Processor: -> Pairs: F(x:S,f(a,a)) -> F(f(f(a,a),a),f(x:S,a)) -> Rules: f(x:S,f(a,a)) -> f(f(f(a,a),a),f(x:S,a)) -> Usable rules: f(x:S,f(a,a)) -> f(f(f(a,a),a),f(x:S,a)) ->Interpretation type: Simple mixed ->Coefficients: All rationals ->Dimension: 1 ->Bound: 2 ->Interpretation: [f](X1,X2) = 1/2.X1.X2 + 1/2.X2 [a] = 1/2 [fSNonEmpty] = 0 [F](X1,X2) = 1/2.X1.X2 + 1/2.X1 + 2.X2 Problem 1: SCC Processor: -> Pairs: Empty -> Rules: f(x:S,f(a,a)) -> f(f(f(a,a),a),f(x:S,a)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. popout

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