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TRS Stand 20472 pair #381712178
details
property
value
status
complete
benchmark
jw38.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n102.star.cs.uiowa.edu
space
Zantema_05
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
0.679903030396 seconds
cpu usage
0.552836365
max memory
6590464.0
stage attributes
key
value
output-size
3064
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(f(a,x),a) -> f(f(f(a,a),f(x,a)),a) ) Problem 1: Innermost Equivalent Processor: -> Rules: f(f(a,x),a) -> f(f(f(a,a),f(x,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),a) -> F(f(f(a,a),f(x,a)),a) F(f(a,x),a) -> F(f(a,a),f(x,a)) F(f(a,x),a) -> F(x,a) -> Rules: f(f(a,x),a) -> f(f(f(a,a),f(x,a)),a) Problem 1: SCC Processor: -> Pairs: F(f(a,x),a) -> F(f(f(a,a),f(x,a)),a) F(f(a,x),a) -> F(f(a,a),f(x,a)) F(f(a,x),a) -> F(x,a) -> Rules: f(f(a,x),a) -> f(f(f(a,a),f(x,a)),a) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(f(a,x),a) -> F(f(f(a,a),f(x,a)),a) F(f(a,x),a) -> F(f(a,a),f(x,a)) F(f(a,x),a) -> F(x,a) ->->-> Rules: f(f(a,x),a) -> f(f(f(a,a),f(x,a)),a) Problem 1: Reduction Pairs Processor: -> Pairs: F(f(a,x),a) -> F(f(f(a,a),f(x,a)),a) F(f(a,x),a) -> F(f(a,a),f(x,a)) F(f(a,x),a) -> F(x,a) -> Rules: f(f(a,x),a) -> f(f(f(a,a),f(x,a)),a) -> Usable rules: f(f(a,x),a) -> f(f(f(a,a),f(x,a)),a) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [f](X1,X2) = 1 [a] = 2 [F](X1,X2) = 2.X2 Problem 1: SCC Processor: -> Pairs: F(f(a,x),a) -> F(f(f(a,a),f(x,a)),a) F(f(a,x),a) -> F(x,a) -> Rules: f(f(a,x),a) -> f(f(f(a,a),f(x,a)),a) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(f(a,x),a) -> F(f(f(a,a),f(x,a)),a) F(f(a,x),a) -> F(x,a) ->->-> Rules: f(f(a,x),a) -> f(f(f(a,a),f(x,a)),a) Problem 1: Reduction Pairs Processor: -> Pairs: F(f(a,x),a) -> F(f(f(a,a),f(x,a)),a) F(f(a,x),a) -> F(x,a) -> Rules: f(f(a,x),a) -> f(f(f(a,a),f(x,a)),a)
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