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TRS Standard pair #487068584
details
property
value
status
complete
benchmark
jw07.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)
0.130617 seconds
cpu usage
0.112998
user time
0.056492
system time
0.056506
max virtual memory
113188.0
max residence set size
5460.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S) (RULES f(a,f(x:S,a)) -> f(a,f(x:S,f(f(a,a),a))) ) Problem 1: Innermost Equivalent Processor: -> Rules: f(a,f(x:S,a)) -> f(a,f(x:S,f(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(a,f(x:S,a)) -> F(a,f(x:S,f(f(a,a),a))) F(a,f(x:S,a)) -> F(x:S,f(f(a,a),a)) -> Rules: f(a,f(x:S,a)) -> f(a,f(x:S,f(f(a,a),a))) Problem 1: SCC Processor: -> Pairs: F(a,f(x:S,a)) -> F(a,f(x:S,f(f(a,a),a))) F(a,f(x:S,a)) -> F(x:S,f(f(a,a),a)) -> Rules: f(a,f(x:S,a)) -> f(a,f(x:S,f(f(a,a),a))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(a,f(x:S,a)) -> F(a,f(x:S,f(f(a,a),a))) F(a,f(x:S,a)) -> F(x:S,f(f(a,a),a)) ->->-> Rules: f(a,f(x:S,a)) -> f(a,f(x:S,f(f(a,a),a))) Problem 1: Reduction Pairs Processor: -> Pairs: F(a,f(x:S,a)) -> F(a,f(x:S,f(f(a,a),a))) F(a,f(x:S,a)) -> F(x:S,f(f(a,a),a)) -> Rules: f(a,f(x:S,a)) -> f(a,f(x:S,f(f(a,a),a))) -> Usable rules: f(a,f(x:S,a)) -> f(a,f(x:S,f(f(a,a),a))) ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 2 ->Interpretation: [f](X1,X2) = 1/2.X2 [a] = 2 [fSNonEmpty] = 0 [F](X1,X2) = 2.X2 Problem 1: SCC Processor: -> Pairs: F(a,f(x:S,a)) -> F(x:S,f(f(a,a),a)) -> Rules: f(a,f(x:S,a)) -> f(a,f(x:S,f(f(a,a),a))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(a,f(x:S,a)) -> F(x:S,f(f(a,a),a)) ->->-> Rules: f(a,f(x:S,a)) -> f(a,f(x:S,f(f(a,a),a))) Problem 1: Reduction Pairs Processor: -> Pairs: F(a,f(x:S,a)) -> F(x:S,f(f(a,a),a)) -> Rules: f(a,f(x:S,a)) -> f(a,f(x:S,f(f(a,a),a))) -> Usable rules: f(a,f(x:S,a)) -> f(a,f(x:S,f(f(a,a),a))) ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 2 ->Interpretation:
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