0.00/0.13 YES 0.00/0.13 0.00/0.13 Problem 1: 0.00/0.13 0.00/0.13 (VAR v_NonEmpty:S X:S X1:S X2:S Y:S) 0.00/0.13 (RULES 0.00/0.13 a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) 0.00/0.13 a__f(X1:S,X2:S) -> f(X1:S,X2:S) 0.00/0.13 mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) 0.00/0.13 mark(g(X:S)) -> g(mark(X:S)) 0.00/0.13 ) 0.00/0.13 (STRATEGY INNERMOST) 0.00/0.13 0.00/0.13 Problem 1: 0.00/0.13 0.00/0.13 Dependency Pairs Processor: 0.00/0.13 -> Pairs: 0.00/0.13 A__F(g(X:S),Y:S) -> A__F(mark(X:S),f(g(X:S),Y:S)) 0.00/0.13 A__F(g(X:S),Y:S) -> MARK(X:S) 0.00/0.13 MARK(f(X1:S,X2:S)) -> A__F(mark(X1:S),X2:S) 0.00/0.13 MARK(f(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.13 MARK(g(X:S)) -> MARK(X:S) 0.00/0.13 -> Rules: 0.00/0.13 a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) 0.00/0.13 a__f(X1:S,X2:S) -> f(X1:S,X2:S) 0.00/0.13 mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) 0.00/0.13 mark(g(X:S)) -> g(mark(X:S)) 0.00/0.13 0.00/0.13 Problem 1: 0.00/0.13 0.00/0.13 SCC Processor: 0.00/0.13 -> Pairs: 0.00/0.13 A__F(g(X:S),Y:S) -> A__F(mark(X:S),f(g(X:S),Y:S)) 0.00/0.13 A__F(g(X:S),Y:S) -> MARK(X:S) 0.00/0.13 MARK(f(X1:S,X2:S)) -> A__F(mark(X1:S),X2:S) 0.00/0.13 MARK(f(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.13 MARK(g(X:S)) -> MARK(X:S) 0.00/0.13 -> Rules: 0.00/0.13 a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) 0.00/0.13 a__f(X1:S,X2:S) -> f(X1:S,X2:S) 0.00/0.13 mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) 0.00/0.13 mark(g(X:S)) -> g(mark(X:S)) 0.00/0.13 ->Strongly Connected Components: 0.00/0.13 ->->Cycle: 0.00/0.13 ->->-> Pairs: 0.00/0.13 A__F(g(X:S),Y:S) -> A__F(mark(X:S),f(g(X:S),Y:S)) 0.00/0.13 A__F(g(X:S),Y:S) -> MARK(X:S) 0.00/0.13 MARK(f(X1:S,X2:S)) -> A__F(mark(X1:S),X2:S) 0.00/0.13 MARK(f(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.13 MARK(g(X:S)) -> MARK(X:S) 0.00/0.13 ->->-> Rules: 0.00/0.13 a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) 0.00/0.13 a__f(X1:S,X2:S) -> f(X1:S,X2:S) 0.00/0.13 mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) 0.00/0.13 mark(g(X:S)) -> g(mark(X:S)) 0.00/0.13 0.00/0.13 Problem 1: 0.00/0.13 0.00/0.13 Reduction Pairs Processor: 0.00/0.13 -> Pairs: 0.00/0.13 A__F(g(X:S),Y:S) -> A__F(mark(X:S),f(g(X:S),Y:S)) 0.00/0.13 A__F(g(X:S),Y:S) -> MARK(X:S) 0.00/0.13 MARK(f(X1:S,X2:S)) -> A__F(mark(X1:S),X2:S) 0.00/0.13 MARK(f(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.13 MARK(g(X:S)) -> MARK(X:S) 0.00/0.13 -> Rules: 0.00/0.13 a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) 0.00/0.13 a__f(X1:S,X2:S) -> f(X1:S,X2:S) 0.00/0.13 mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) 0.00/0.13 mark(g(X:S)) -> g(mark(X:S)) 0.00/0.13 -> Usable rules: 0.00/0.13 a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) 0.00/0.13 a__f(X1:S,X2:S) -> f(X1:S,X2:S) 0.00/0.13 mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) 0.00/0.13 mark(g(X:S)) -> g(mark(X:S)) 0.00/0.13 ->Interpretation type: 0.00/0.13 Linear 0.00/0.13 ->Coefficients: 0.00/0.13 Natural Numbers 0.00/0.13 ->Dimension: 0.00/0.13 1 0.00/0.13 ->Bound: 0.00/0.13 2 0.00/0.13 ->Interpretation: 0.00/0.13 0.00/0.13 [a__f](X1,X2) = 2.X1 + 2 0.00/0.13 [mark](X) = X 0.00/0.13 [f](X1,X2) = 2.X1 + 2 0.00/0.13 [fSNonEmpty] = 0 0.00/0.13 [g](X) = X + 1 0.00/0.13 [A__F](X1,X2) = 2.X1 + 2 0.00/0.13 [MARK](X) = 2.X + 1 0.00/0.13 0.00/0.13 Problem 1: 0.00/0.13 0.00/0.13 SCC Processor: 0.00/0.13 -> Pairs: 0.00/0.13 A__F(g(X:S),Y:S) -> MARK(X:S) 0.00/0.13 MARK(f(X1:S,X2:S)) -> A__F(mark(X1:S),X2:S) 0.00/0.13 MARK(f(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.13 MARK(g(X:S)) -> MARK(X:S) 0.00/0.13 -> Rules: 0.00/0.13 a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) 0.00/0.13 a__f(X1:S,X2:S) -> f(X1:S,X2:S) 0.00/0.13 mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) 0.00/0.13 mark(g(X:S)) -> g(mark(X:S)) 0.00/0.13 ->Strongly Connected Components: 0.00/0.13 ->->Cycle: 0.00/0.13 ->->-> Pairs: 0.00/0.13 A__F(g(X:S),Y:S) -> MARK(X:S) 0.00/0.13 MARK(f(X1:S,X2:S)) -> A__F(mark(X1:S),X2:S) 0.00/0.13 MARK(f(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.13 MARK(g(X:S)) -> MARK(X:S) 0.00/0.13 ->->-> Rules: 0.00/0.13 a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) 0.00/0.13 a__f(X1:S,X2:S) -> f(X1:S,X2:S) 0.00/0.13 mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) 0.00/0.13 mark(g(X:S)) -> g(mark(X:S)) 0.00/0.13 0.00/0.13 Problem 1: 0.00/0.13 0.00/0.13 Reduction Pairs Processor: 0.00/0.13 -> Pairs: 0.00/0.13 A__F(g(X:S),Y:S) -> MARK(X:S) 0.00/0.13 MARK(f(X1:S,X2:S)) -> A__F(mark(X1:S),X2:S) 0.00/0.13 MARK(f(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.13 MARK(g(X:S)) -> MARK(X:S) 0.00/0.13 -> Rules: 0.00/0.13 a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) 0.00/0.13 a__f(X1:S,X2:S) -> f(X1:S,X2:S) 0.00/0.13 mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) 0.00/0.13 mark(g(X:S)) -> g(mark(X:S)) 0.00/0.13 -> Usable rules: 0.00/0.13 a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) 0.00/0.13 a__f(X1:S,X2:S) -> f(X1:S,X2:S) 0.00/0.13 mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) 0.00/0.13 mark(g(X:S)) -> g(mark(X:S)) 0.00/0.13 ->Interpretation type: 0.00/0.13 Linear 0.00/0.13 ->Coefficients: 0.00/0.13 Natural Numbers 0.00/0.13 ->Dimension: 0.00/0.13 1 0.00/0.13 ->Bound: 0.00/0.13 2 0.00/0.13 ->Interpretation: 0.00/0.13 0.00/0.13 [a__f](X1,X2) = X1 + 2 0.00/0.13 [mark](X) = 2.X + 2 0.00/0.13 [f](X1,X2) = X1 + 2 0.00/0.13 [fSNonEmpty] = 0 0.00/0.13 [g](X) = 2.X + 2 0.00/0.13 [A__F](X1,X2) = X1 + 2 0.00/0.13 [MARK](X) = 2.X + 2 0.00/0.13 0.00/0.13 Problem 1: 0.00/0.13 0.00/0.13 SCC Processor: 0.00/0.13 -> Pairs: 0.00/0.13 MARK(f(X1:S,X2:S)) -> A__F(mark(X1:S),X2:S) 0.00/0.13 MARK(f(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.13 MARK(g(X:S)) -> MARK(X:S) 0.00/0.13 -> Rules: 0.00/0.13 a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) 0.00/0.13 a__f(X1:S,X2:S) -> f(X1:S,X2:S) 0.00/0.13 mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) 0.00/0.13 mark(g(X:S)) -> g(mark(X:S)) 0.00/0.13 ->Strongly Connected Components: 0.00/0.13 ->->Cycle: 0.00/0.13 ->->-> Pairs: 0.00/0.13 MARK(f(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.13 MARK(g(X:S)) -> MARK(X:S) 0.00/0.13 ->->-> Rules: 0.00/0.13 a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) 0.00/0.13 a__f(X1:S,X2:S) -> f(X1:S,X2:S) 0.00/0.13 mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) 0.00/0.13 mark(g(X:S)) -> g(mark(X:S)) 0.00/0.13 0.00/0.13 Problem 1: 0.00/0.13 0.00/0.13 Subterm Processor: 0.00/0.13 -> Pairs: 0.00/0.13 MARK(f(X1:S,X2:S)) -> MARK(X1:S) 0.00/0.13 MARK(g(X:S)) -> MARK(X:S) 0.00/0.13 -> Rules: 0.00/0.13 a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) 0.00/0.13 a__f(X1:S,X2:S) -> f(X1:S,X2:S) 0.00/0.13 mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) 0.00/0.13 mark(g(X:S)) -> g(mark(X:S)) 0.00/0.13 ->Projection: 0.00/0.13 pi(MARK) = 1 0.00/0.13 0.00/0.13 Problem 1: 0.00/0.13 0.00/0.13 SCC Processor: 0.00/0.13 -> Pairs: 0.00/0.13 Empty 0.00/0.13 -> Rules: 0.00/0.13 a__f(g(X:S),Y:S) -> a__f(mark(X:S),f(g(X:S),Y:S)) 0.00/0.13 a__f(X1:S,X2:S) -> f(X1:S,X2:S) 0.00/0.13 mark(f(X1:S,X2:S)) -> a__f(mark(X1:S),X2:S) 0.00/0.13 mark(g(X:S)) -> g(mark(X:S)) 0.00/0.13 ->Strongly Connected Components: 0.00/0.13 There is no strongly connected component 0.00/0.13 0.00/0.13 The problem is finite. 0.00/0.13 EOF