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TRS Innermost pair #487093574
details
property
value
status
complete
benchmark
test75.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
Mixed_innermost
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
20.1965 seconds
cpu usage
20.1558
user time
18.8077
system time
1.34806
max virtual memory
599076.0
max residence set size
5736.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S X:S Y:S) (RULES f(0,1,X:S) -> f(g(X:S,X:S),X:S,X:S) g(X:S,Y:S) -> X:S g(X:S,Y:S) -> Y:S ) (STRATEGY INNERMOST) Problem 1: Dependency Pairs Processor: -> Pairs: F(0,1,X:S) -> F(g(X:S,X:S),X:S,X:S) F(0,1,X:S) -> G(X:S,X:S) -> Rules: f(0,1,X:S) -> f(g(X:S,X:S),X:S,X:S) g(X:S,Y:S) -> X:S g(X:S,Y:S) -> Y:S Problem 1: SCC Processor: -> Pairs: F(0,1,X:S) -> F(g(X:S,X:S),X:S,X:S) F(0,1,X:S) -> G(X:S,X:S) -> Rules: f(0,1,X:S) -> f(g(X:S,X:S),X:S,X:S) g(X:S,Y:S) -> X:S g(X:S,Y:S) -> Y:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(0,1,X:S) -> F(g(X:S,X:S),X:S,X:S) ->->-> Rules: f(0,1,X:S) -> f(g(X:S,X:S),X:S,X:S) g(X:S,Y:S) -> X:S g(X:S,Y:S) -> Y:S Problem 1: Instantiation Processor: -> Pairs: F(0,1,X:S) -> F(g(X:S,X:S),X:S,X:S) -> Rules: f(0,1,X:S) -> f(g(X:S,X:S),X:S,X:S) g(X:S,Y:S) -> X:S g(X:S,Y:S) -> Y:S ->Instantiated Pairs: ->->Original Pair: F(0,1,X:S) -> F(g(X:S,X:S),X:S,X:S) ->-> Instantiated pairs: F(0,1,1) -> F(g(1,1),1,1) Problem 1: SCC Processor: -> Pairs: F(0,1,1) -> F(g(1,1),1,1) -> Rules: f(0,1,X:S) -> f(g(X:S,X:S),X:S,X:S) g(X:S,Y:S) -> X:S g(X:S,Y:S) -> Y:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(0,1,1) -> F(g(1,1),1,1) ->->-> Rules: f(0,1,X:S) -> f(g(X:S,X:S),X:S,X:S) g(X:S,Y:S) -> X:S g(X:S,Y:S) -> Y:S Problem 1: Reduction Pairs Processor: -> Pairs: F(0,1,1) -> F(g(1,1),1,1) -> Rules: f(0,1,X:S) -> f(g(X:S,X:S),X:S,X:S) g(X:S,Y:S) -> X:S g(X:S,Y:S) -> Y:S -> Usable rules: g(X:S,Y:S) -> X:S g(X:S,Y:S) -> Y:S ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [f](X1,X2,X3) = 0 [g](X1,X2) = X1 + 2.X2 + 1 [0] = 2
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