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TRS Stand 20472 pair #381712418
details
property
value
status
complete
benchmark
2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n074.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.644410848618 seconds
cpu usage
0.420218402
max memory
5877760.0
stage attributes
key
value
output-size
2166
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 x) (RULES f(a,f(f(a,a),x)) -> f(f(a,a),f(a,f(a,x))) ) Problem 1: Innermost Equivalent Processor: -> Rules: f(a,f(f(a,a),x)) -> f(f(a,a),f(a,f(a,x))) -> 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(f(a,a),x)) -> F(f(a,a),f(a,f(a,x))) F(a,f(f(a,a),x)) -> F(a,f(a,x)) F(a,f(f(a,a),x)) -> F(a,x) -> Rules: f(a,f(f(a,a),x)) -> f(f(a,a),f(a,f(a,x))) Problem 1: SCC Processor: -> Pairs: F(a,f(f(a,a),x)) -> F(f(a,a),f(a,f(a,x))) F(a,f(f(a,a),x)) -> F(a,f(a,x)) F(a,f(f(a,a),x)) -> F(a,x) -> Rules: f(a,f(f(a,a),x)) -> f(f(a,a),f(a,f(a,x))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(a,f(f(a,a),x)) -> F(a,f(a,x)) F(a,f(f(a,a),x)) -> F(a,x) ->->-> Rules: f(a,f(f(a,a),x)) -> f(f(a,a),f(a,f(a,x))) Problem 1: Reduction Pairs Processor: -> Pairs: F(a,f(f(a,a),x)) -> F(a,f(a,x)) F(a,f(f(a,a),x)) -> F(a,x) -> Rules: f(a,f(f(a,a),x)) -> f(f(a,a),f(a,f(a,x))) -> Usable rules: f(a,f(f(a,a),x)) -> f(f(a,a),f(a,f(a,x))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 2 ->Bound: 1 ->Interpretation: [f](X1,X2) = [0 0;1 0].X1 + [0 0;0 1].X2 + [1;0] [a] = 0 [F](X1,X2) = [0 1;0 1].X2 Problem 1: SCC Processor: -> Pairs: F(a,f(f(a,a),x)) -> F(a,x) -> Rules: f(a,f(f(a,a),x)) -> f(f(a,a),f(a,f(a,x))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(a,f(f(a,a),x)) -> F(a,x) ->->-> Rules: f(a,f(f(a,a),x)) -> f(f(a,a),f(a,f(a,x))) Problem 1: Subterm Processor: -> Pairs: F(a,f(f(a,a),x)) -> F(a,x) -> Rules: f(a,f(f(a,a),x)) -> f(f(a,a),f(a,f(a,x))) ->Projection: pi(F) = 2 Problem 1:
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