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TRS Standard pair #487073509
details
property
value
status
complete
benchmark
jwteparla1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n177.star.cs.uiowa.edu
space
Waldmann_06
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
9.7871 seconds
cpu usage
9.70799
user time
8.58932
system time
1.11867
max virtual memory
708668.0
max residence set size
6360.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S) (RULES f(x:S,f(a,f(f(a,a),a))) -> f(f(a,x:S),x:S) ) Problem 1: Innermost Equivalent Processor: -> Rules: f(x:S,f(a,f(f(a,a),a))) -> f(f(a,x:S),x:S) -> 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,f(f(a,a),a))) -> F(f(a,x:S),x:S) F(x:S,f(a,f(f(a,a),a))) -> F(a,x:S) -> Rules: f(x:S,f(a,f(f(a,a),a))) -> f(f(a,x:S),x:S) Problem 1: SCC Processor: -> Pairs: F(x:S,f(a,f(f(a,a),a))) -> F(f(a,x:S),x:S) F(x:S,f(a,f(f(a,a),a))) -> F(a,x:S) -> Rules: f(x:S,f(a,f(f(a,a),a))) -> f(f(a,x:S),x:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(x:S,f(a,f(f(a,a),a))) -> F(f(a,x:S),x:S) F(x:S,f(a,f(f(a,a),a))) -> F(a,x:S) ->->-> Rules: f(x:S,f(a,f(f(a,a),a))) -> f(f(a,x:S),x:S) Problem 1: Reduction Pairs Processor: -> Pairs: F(x:S,f(a,f(f(a,a),a))) -> F(f(a,x:S),x:S) F(x:S,f(a,f(f(a,a),a))) -> F(a,x:S) -> Rules: f(x:S,f(a,f(f(a,a),a))) -> f(f(a,x:S),x:S) -> Usable rules: f(x:S,f(a,f(f(a,a),a))) -> f(f(a,x:S),x:S) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [f](X1,X2) = 2 [a] = 1 [fSNonEmpty] = 0 [F](X1,X2) = 2.X1 + 2.X2 Problem 1: SCC Processor: -> Pairs: F(x:S,f(a,f(f(a,a),a))) -> F(f(a,x:S),x:S) -> Rules: f(x:S,f(a,f(f(a,a),a))) -> f(f(a,x:S),x:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(x:S,f(a,f(f(a,a),a))) -> F(f(a,x:S),x:S) ->->-> Rules: f(x:S,f(a,f(f(a,a),a))) -> f(f(a,x:S),x:S) Problem 1: Reduction Pair Processor: -> Pairs: F(x:S,f(a,f(f(a,a),a))) -> F(f(a,x:S),x:S) -> Rules: f(x:S,f(a,f(f(a,a),a))) -> f(f(a,x:S),x:S) -> Usable rules: f(x:S,f(a,f(f(a,a),a))) -> f(f(a,x:S),x:S) ->Mace4 Output: ============================== Mace4 ================================= Mace4 (64) version 2009-11A, November 2009. Process 60326 was started by sandbox2 on n177.star.cs.uiowa.edu, Mon Jun 22 10:25:08 2020 The command was "./mace4 -c -f /tmp/mace41315634022635723058.in". ============================== end of head =========================== ============================== INPUT =================================
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