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TRS Standard pair #487069029
details
property
value
status
complete
benchmark
5.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n070.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0646431 seconds
cpu usage
0.054304
user time
0.021031
system time
0.033273
max virtual memory
113188.0
max residence set size
4704.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S) (RULES f(x:S,f(a,a)) -> f(f(x:S,a),x:S) ) Problem 1: Innermost Equivalent Processor: -> Rules: f(x:S,f(a,a)) -> f(f(x:S,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(x:S,f(a,a)) -> F(f(x:S,a),x:S) -> Rules: f(x:S,f(a,a)) -> f(f(x:S,a),x:S) Problem 1: SCC Processor: -> Pairs: F(x:S,f(a,a)) -> F(f(x:S,a),x:S) -> Rules: f(x:S,f(a,a)) -> f(f(x:S,a),x:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(x:S,f(a,a)) -> F(f(x:S,a),x:S) ->->-> Rules: f(x:S,f(a,a)) -> f(f(x:S,a),x:S) Problem 1: Reduction Pairs Processor: -> Pairs: F(x:S,f(a,a)) -> F(f(x:S,a),x:S) -> Rules: f(x:S,f(a,a)) -> f(f(x:S,a),x:S) -> Usable rules: f(x:S,f(a,a)) -> f(f(x:S,a),x:S) ->Interpretation type: Linear ->Coefficients: All rationals ->Dimension: 1 ->Bound: 2 ->Interpretation: [f](X1,X2) = 1/2.X1 [a] = 1/2 [fSNonEmpty] = 0 [F](X1,X2) = 2.X1 + X2 Problem 1: SCC Processor: -> Pairs: Empty -> Rules: f(x:S,f(a,a)) -> f(f(x:S,a),x:S) ->Strongly Connected Components: There is no strongly connected component The problem is finite.
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