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TRS Innermost pair #487093202
details
property
value
status
complete
benchmark
Ex4_4_Luc96b_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n137.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0601539 seconds
cpu usage
0.064104
user time
0.032304
system time
0.0318
max virtual memory
113188.0
max residence set size
5440.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S X:S X1:S X2:S Y:S) (RULES a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) a__f(X1:S,X2:S) -> f(X1:S,X2:S) mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) mark(g(X:S)) -> g(mark(X:S)) ) (STRATEGY INNERMOST) Problem 1: Dependency Pairs Processor: -> Pairs: A__F(g(X:S),Y:S) -> A__F(mark(X:S),f(g(X:S),Y:S)) A__F(g(X:S),Y:S) -> MARK(X:S) MARK(f(X1:S,X2:S)) -> A__F(mark(X1:S),X2:S) MARK(f(X1:S,X2:S)) -> MARK(X1:S) MARK(g(X:S)) -> MARK(X:S) -> Rules: a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) a__f(X1:S,X2:S) -> f(X1:S,X2:S) mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) mark(g(X:S)) -> g(mark(X:S)) Problem 1: SCC Processor: -> Pairs: A__F(g(X:S),Y:S) -> A__F(mark(X:S),f(g(X:S),Y:S)) A__F(g(X:S),Y:S) -> MARK(X:S) MARK(f(X1:S,X2:S)) -> A__F(mark(X1:S),X2:S) MARK(f(X1:S,X2:S)) -> MARK(X1:S) MARK(g(X:S)) -> MARK(X:S) -> Rules: a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) a__f(X1:S,X2:S) -> f(X1:S,X2:S) mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) mark(g(X:S)) -> g(mark(X:S)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: A__F(g(X:S),Y:S) -> A__F(mark(X:S),f(g(X:S),Y:S)) A__F(g(X:S),Y:S) -> MARK(X:S) MARK(f(X1:S,X2:S)) -> A__F(mark(X1:S),X2:S) MARK(f(X1:S,X2:S)) -> MARK(X1:S) MARK(g(X:S)) -> MARK(X:S) ->->-> Rules: a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) a__f(X1:S,X2:S) -> f(X1:S,X2:S) mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) mark(g(X:S)) -> g(mark(X:S)) Problem 1: Reduction Pairs Processor: -> Pairs: A__F(g(X:S),Y:S) -> A__F(mark(X:S),f(g(X:S),Y:S)) A__F(g(X:S),Y:S) -> MARK(X:S) MARK(f(X1:S,X2:S)) -> A__F(mark(X1:S),X2:S) MARK(f(X1:S,X2:S)) -> MARK(X1:S) MARK(g(X:S)) -> MARK(X:S) -> Rules: a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) a__f(X1:S,X2:S) -> f(X1:S,X2:S) mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) mark(g(X:S)) -> g(mark(X:S)) -> Usable rules: a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) a__f(X1:S,X2:S) -> f(X1:S,X2:S) mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) mark(g(X:S)) -> g(mark(X:S)) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [a__f](X1,X2) = 2.X1 + 2 [mark](X) = X [f](X1,X2) = 2.X1 + 2 [fSNonEmpty] = 0 [g](X) = X + 1 [A__F](X1,X2) = 2.X1 + 2 [MARK](X) = 2.X + 1 Problem 1: SCC Processor: -> Pairs: A__F(g(X:S),Y:S) -> MARK(X:S) MARK(f(X1:S,X2:S)) -> A__F(mark(X1:S),X2:S) MARK(f(X1:S,X2:S)) -> MARK(X1:S)
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