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TRS Standard pair #516965366
details
property
value
status
complete
benchmark
jw30.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n003.star.cs.uiowa.edu
space
Zantema_05
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
1.43690109253 seconds
cpu usage
1.294408346
max memory
7200768.0
stage attributes
key
value
output-size
2422
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S x:S) (RULES f(f(a,a),x:S) -> f(f(x:S,a),f(a,f(a,a))) ) Problem 1: Innermost Equivalent Processor: -> Rules: f(f(a,a),x:S) -> f(f(x:S,a),f(a,f(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,a),x:S) -> F(f(x:S,a),f(a,f(a,a))) F(f(a,a),x:S) -> F(x:S,a) -> Rules: f(f(a,a),x:S) -> f(f(x:S,a),f(a,f(a,a))) Problem 1: SCC Processor: -> Pairs: F(f(a,a),x:S) -> F(f(x:S,a),f(a,f(a,a))) F(f(a,a),x:S) -> F(x:S,a) -> Rules: f(f(a,a),x:S) -> f(f(x:S,a),f(a,f(a,a))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(f(a,a),x:S) -> F(f(x:S,a),f(a,f(a,a))) F(f(a,a),x:S) -> F(x:S,a) ->->-> Rules: f(f(a,a),x:S) -> f(f(x:S,a),f(a,f(a,a))) Problem 1: Reduction Pairs Processor: -> Pairs: F(f(a,a),x:S) -> F(f(x:S,a),f(a,f(a,a))) F(f(a,a),x:S) -> F(x:S,a) -> Rules: f(f(a,a),x:S) -> f(f(x:S,a),f(a,f(a,a))) -> Usable rules: f(f(a,a),x:S) -> f(f(x:S,a),f(a,f(a,a))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 2 ->Bound: 1 ->Interpretation: [f](X1,X2) = [0 1;0 0].X1 + [0 1;0 0].X2 [a] = [0;1] [fSNonEmpty] = 0 [F](X1,X2) = [1 0;1 1].X1 + [1 1;1 1].X2 Problem 1: SCC Processor: -> Pairs: F(f(a,a),x:S) -> F(f(x:S,a),f(a,f(a,a))) -> Rules: f(f(a,a),x:S) -> f(f(x:S,a),f(a,f(a,a))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(f(a,a),x:S) -> F(f(x:S,a),f(a,f(a,a))) ->->-> Rules: f(f(a,a),x:S) -> f(f(x:S,a),f(a,f(a,a))) Problem 1: Reduction Pairs Processor: -> Pairs: F(f(a,a),x:S) -> F(f(x:S,a),f(a,f(a,a))) -> Rules: f(f(a,a),x:S) -> f(f(x:S,a),f(a,f(a,a))) -> Usable rules: f(f(a,a),x:S) -> f(f(x:S,a),f(a,f(a,a))) ->Interpretation type: Linear ->Coefficients: All rationals
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