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TRS Standard pair #487068484
details
property
value
status
complete
benchmark
jw33.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n073.star.cs.uiowa.edu
space
Zantema_05
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.338527 seconds
cpu usage
0.319622
user time
0.254056
system time
0.065566
max virtual memory
113188.0
max residence set size
5468.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S) (RULES f(f(a,x:S),a) -> f(f(a,f(a,f(a,a))),x:S) ) Problem 1: Innermost Equivalent Processor: -> Rules: f(f(a,x:S),a) -> f(f(a,f(a,f(a,a))),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(f(a,x:S),a) -> F(f(a,f(a,f(a,a))),x:S) -> Rules: f(f(a,x:S),a) -> f(f(a,f(a,f(a,a))),x:S) Problem 1: SCC Processor: -> Pairs: F(f(a,x:S),a) -> F(f(a,f(a,f(a,a))),x:S) -> Rules: f(f(a,x:S),a) -> f(f(a,f(a,f(a,a))),x:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(f(a,x:S),a) -> F(f(a,f(a,f(a,a))),x:S) ->->-> Rules: f(f(a,x:S),a) -> f(f(a,f(a,f(a,a))),x:S) Problem 1: Reduction Pairs Processor: -> Pairs: F(f(a,x:S),a) -> F(f(a,f(a,f(a,a))),x:S) -> Rules: f(f(a,x:S),a) -> f(f(a,f(a,f(a,a))),x:S) -> Usable rules: f(f(a,x:S),a) -> f(f(a,f(a,f(a,a))),x:S) ->Interpretation type: Simple mixed ->Coefficients: All rationals ->Dimension: 1 ->Bound: 2 ->Interpretation: [f](X1,X2) = 1/2.X1.X2 [a] = 1 [fSNonEmpty] = 0 [F](X1,X2) = 2.X1.X2 + 1/2.X1 + X2 Problem 1: SCC Processor: -> Pairs: Empty -> Rules: f(f(a,x:S),a) -> f(f(a,f(a,f(a,a))),x:S) ->Strongly Connected Components: There is no strongly connected component The problem is finite.
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