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TRS Standard pair #487069049
details
property
value
status
complete
benchmark
test1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n183.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0981269 seconds
cpu usage
0.085457
user time
0.034709
system time
0.050748
max virtual memory
113188.0
max residence set size
5476.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES f(s(x:S),y:S) -> f(x:S,s(s(x:S))) f(x:S,s(s(y:S))) -> f(y:S,x:S) ) Problem 1: Dependency Pairs Processor: -> Pairs: F(s(x:S),y:S) -> F(x:S,s(s(x:S))) F(x:S,s(s(y:S))) -> F(y:S,x:S) -> Rules: f(s(x:S),y:S) -> f(x:S,s(s(x:S))) f(x:S,s(s(y:S))) -> f(y:S,x:S) Problem 1: SCC Processor: -> Pairs: F(s(x:S),y:S) -> F(x:S,s(s(x:S))) F(x:S,s(s(y:S))) -> F(y:S,x:S) -> Rules: f(s(x:S),y:S) -> f(x:S,s(s(x:S))) f(x:S,s(s(y:S))) -> f(y:S,x:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(s(x:S),y:S) -> F(x:S,s(s(x:S))) F(x:S,s(s(y:S))) -> F(y:S,x:S) ->->-> Rules: f(s(x:S),y:S) -> f(x:S,s(s(x:S))) f(x:S,s(s(y:S))) -> f(y:S,x:S) Problem 1: Reduction Pair Processor: -> Pairs: F(s(x:S),y:S) -> F(x:S,s(s(x:S))) F(x:S,s(s(y:S))) -> F(y:S,x:S) -> Rules: f(s(x:S),y:S) -> f(x:S,s(s(x:S))) f(x:S,s(s(y:S))) -> f(y:S,x:S) -> Usable rules: Empty ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 2 ->Interpretation: [s](X) = 2.X + 2 [F](X1,X2) = 2.X1 + 1/2.X2 Problem 1: SCC Processor: -> Pairs: F(x:S,s(s(y:S))) -> F(y:S,x:S) -> Rules: f(s(x:S),y:S) -> f(x:S,s(s(x:S))) f(x:S,s(s(y:S))) -> f(y:S,x:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(x:S,s(s(y:S))) -> F(y:S,x:S) ->->-> Rules: f(s(x:S),y:S) -> f(x:S,s(s(x:S))) f(x:S,s(s(y:S))) -> f(y:S,x:S) Problem 1: Reduction Pair Processor: -> Pairs: F(x:S,s(s(y:S))) -> F(y:S,x:S) -> Rules: f(s(x:S),y:S) -> f(x:S,s(s(x:S))) f(x:S,s(s(y:S))) -> f(y:S,x:S) -> Usable rules: Empty ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [s](X) = 2.X + 2 [F](X1,X2) = 2.X1 + 2.X2
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