0.22/0.65 YES 0.22/0.65 0.22/0.65 Problem 1: 0.22/0.65 0.22/0.65 (VAR v_NonEmpty:S I:S P:S X:S X1:S X2:S Y:S Z:S) 0.22/0.65 (RULES 0.22/0.65 a__U11(tt) -> a__U12(tt) 0.22/0.65 a__U11(X:S) -> U11(X:S) 0.22/0.65 a__U12(tt) -> tt 0.22/0.65 a__U12(X:S) -> U12(X:S) 0.22/0.65 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.65 a____(nil,X:S) -> mark(X:S) 0.22/0.65 a____(X:S,nil) -> mark(X:S) 0.22/0.65 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.65 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.65 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.65 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.65 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.65 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.65 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.65 mark(nil) -> nil 0.22/0.65 mark(tt) -> tt 0.22/0.65 ) 0.22/0.65 (STRATEGY INNERMOST) 0.22/0.65 0.22/0.65 Problem 1: 0.22/0.65 0.22/0.65 Dependency Pairs Processor: 0.22/0.65 -> Pairs: 0.22/0.65 A__U11(tt) -> A__U12(tt) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 0.22/0.65 A____(nil,X:S) -> MARK(X:S) 0.22/0.65 A____(X:S,nil) -> MARK(X:S) 0.22/0.65 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__U11(tt) 0.22/0.65 MARK(U11(X:S)) -> A__U11(mark(X:S)) 0.22/0.65 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.65 MARK(U12(X:S)) -> A__U12(mark(X:S)) 0.22/0.65 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.65 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 0.22/0.65 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.65 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.65 MARK(isNePal(X:S)) -> A__ISNEPAL(mark(X:S)) 0.22/0.65 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.65 -> Rules: 0.22/0.65 a__U11(tt) -> a__U12(tt) 0.22/0.65 a__U11(X:S) -> U11(X:S) 0.22/0.65 a__U12(tt) -> tt 0.22/0.65 a__U12(X:S) -> U12(X:S) 0.22/0.65 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.65 a____(nil,X:S) -> mark(X:S) 0.22/0.65 a____(X:S,nil) -> mark(X:S) 0.22/0.65 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.65 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.65 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.65 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.65 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.65 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.65 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.65 mark(nil) -> nil 0.22/0.65 mark(tt) -> tt 0.22/0.65 0.22/0.65 Problem 1: 0.22/0.65 0.22/0.65 SCC Processor: 0.22/0.65 -> Pairs: 0.22/0.65 A__U11(tt) -> A__U12(tt) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 0.22/0.65 A____(nil,X:S) -> MARK(X:S) 0.22/0.65 A____(X:S,nil) -> MARK(X:S) 0.22/0.65 A__ISNEPAL(__(I:S,__(P:S,I:S))) -> A__U11(tt) 0.22/0.65 MARK(U11(X:S)) -> A__U11(mark(X:S)) 0.22/0.65 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.65 MARK(U12(X:S)) -> A__U12(mark(X:S)) 0.22/0.65 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.65 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 0.22/0.65 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.65 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.65 MARK(isNePal(X:S)) -> A__ISNEPAL(mark(X:S)) 0.22/0.65 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.65 -> Rules: 0.22/0.65 a__U11(tt) -> a__U12(tt) 0.22/0.65 a__U11(X:S) -> U11(X:S) 0.22/0.65 a__U12(tt) -> tt 0.22/0.65 a__U12(X:S) -> U12(X:S) 0.22/0.65 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.65 a____(nil,X:S) -> mark(X:S) 0.22/0.65 a____(X:S,nil) -> mark(X:S) 0.22/0.65 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.65 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.65 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.65 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.65 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.65 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.65 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.65 mark(nil) -> nil 0.22/0.65 mark(tt) -> tt 0.22/0.65 ->Strongly Connected Components: 0.22/0.65 ->->Cycle: 0.22/0.65 ->->-> Pairs: 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 0.22/0.65 A____(nil,X:S) -> MARK(X:S) 0.22/0.65 A____(X:S,nil) -> MARK(X:S) 0.22/0.65 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.65 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.65 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 0.22/0.65 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.65 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.65 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.65 ->->-> Rules: 0.22/0.65 a__U11(tt) -> a__U12(tt) 0.22/0.65 a__U11(X:S) -> U11(X:S) 0.22/0.65 a__U12(tt) -> tt 0.22/0.65 a__U12(X:S) -> U12(X:S) 0.22/0.65 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.65 a____(nil,X:S) -> mark(X:S) 0.22/0.65 a____(X:S,nil) -> mark(X:S) 0.22/0.65 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.65 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.65 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.65 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.65 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.65 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.65 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.65 mark(nil) -> nil 0.22/0.65 mark(tt) -> tt 0.22/0.65 0.22/0.65 Problem 1: 0.22/0.65 0.22/0.65 Reduction Pairs Processor: 0.22/0.65 -> Pairs: 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 0.22/0.65 A____(nil,X:S) -> MARK(X:S) 0.22/0.65 A____(X:S,nil) -> MARK(X:S) 0.22/0.65 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.65 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.65 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 0.22/0.65 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.65 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.65 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.65 -> Rules: 0.22/0.65 a__U11(tt) -> a__U12(tt) 0.22/0.65 a__U11(X:S) -> U11(X:S) 0.22/0.65 a__U12(tt) -> tt 0.22/0.65 a__U12(X:S) -> U12(X:S) 0.22/0.65 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.65 a____(nil,X:S) -> mark(X:S) 0.22/0.65 a____(X:S,nil) -> mark(X:S) 0.22/0.65 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.65 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.65 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.65 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.65 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.65 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.65 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.65 mark(nil) -> nil 0.22/0.65 mark(tt) -> tt 0.22/0.65 -> Usable rules: 0.22/0.65 a__U11(tt) -> a__U12(tt) 0.22/0.65 a__U11(X:S) -> U11(X:S) 0.22/0.65 a__U12(tt) -> tt 0.22/0.65 a__U12(X:S) -> U12(X:S) 0.22/0.65 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.65 a____(nil,X:S) -> mark(X:S) 0.22/0.65 a____(X:S,nil) -> mark(X:S) 0.22/0.65 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.65 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.65 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.65 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.65 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.65 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.65 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.65 mark(nil) -> nil 0.22/0.65 mark(tt) -> tt 0.22/0.65 ->Interpretation type: 0.22/0.65 Linear 0.22/0.65 ->Coefficients: 0.22/0.65 Natural Numbers 0.22/0.65 ->Dimension: 0.22/0.65 1 0.22/0.65 ->Bound: 0.22/0.65 2 0.22/0.65 ->Interpretation: 0.22/0.65 0.22/0.65 [a__U11](X) = 2.X + 1 0.22/0.65 [a__U12](X) = 2.X + 1 0.22/0.65 [a____](X1,X2) = 2.X1 + X2 + 2 0.22/0.65 [a__isNePal](X) = 2.X 0.22/0.65 [mark](X) = X 0.22/0.65 [U11](X) = 2.X + 1 0.22/0.65 [U12](X) = 2.X + 1 0.22/0.65 [__](X1,X2) = 2.X1 + X2 + 2 0.22/0.65 [fSNonEmpty] = 0 0.22/0.65 [isNePal](X) = 2.X 0.22/0.65 [nil] = 2 0.22/0.65 [tt] = 0 0.22/0.65 [A__U11](X) = 0 0.22/0.65 [A__U12](X) = 0 0.22/0.65 [A____](X1,X2) = 2.X1 + X2 + 1 0.22/0.65 [A__ISNEPAL](X) = 0 0.22/0.65 [MARK](X) = X 0.22/0.65 0.22/0.65 Problem 1: 0.22/0.65 0.22/0.65 SCC Processor: 0.22/0.65 -> Pairs: 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 0.22/0.65 A____(nil,X:S) -> MARK(X:S) 0.22/0.65 A____(X:S,nil) -> MARK(X:S) 0.22/0.65 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.65 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.65 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 0.22/0.65 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.65 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.65 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.65 -> Rules: 0.22/0.65 a__U11(tt) -> a__U12(tt) 0.22/0.65 a__U11(X:S) -> U11(X:S) 0.22/0.65 a__U12(tt) -> tt 0.22/0.65 a__U12(X:S) -> U12(X:S) 0.22/0.65 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.65 a____(nil,X:S) -> mark(X:S) 0.22/0.65 a____(X:S,nil) -> mark(X:S) 0.22/0.65 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.65 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.65 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.65 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.65 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.65 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.65 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.65 mark(nil) -> nil 0.22/0.65 mark(tt) -> tt 0.22/0.65 ->Strongly Connected Components: 0.22/0.65 ->->Cycle: 0.22/0.65 ->->-> Pairs: 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 0.22/0.65 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 0.22/0.65 A____(nil,X:S) -> MARK(X:S) 0.22/0.65 A____(X:S,nil) -> MARK(X:S) 0.22/0.65 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.65 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.65 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 0.22/0.65 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.65 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.65 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.65 ->->-> Rules: 0.22/0.65 a__U11(tt) -> a__U12(tt) 0.22/0.65 a__U11(X:S) -> U11(X:S) 0.22/0.65 a__U12(tt) -> tt 0.22/0.65 a__U12(X:S) -> U12(X:S) 0.22/0.65 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.65 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 0.22/0.66 Problem 1: 0.22/0.66 0.22/0.66 Reduction Pairs Processor: 0.22/0.66 -> Pairs: 0.22/0.66 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S)) 0.22/0.66 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 0.22/0.66 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 0.22/0.66 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 0.22/0.66 A____(nil,X:S) -> MARK(X:S) 0.22/0.66 A____(X:S,nil) -> MARK(X:S) 0.22/0.66 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.66 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.66 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.66 -> Rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 -> Usable rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 ->Interpretation type: 0.22/0.66 Linear 0.22/0.66 ->Coefficients: 0.22/0.66 Natural Numbers 0.22/0.66 ->Dimension: 0.22/0.66 1 0.22/0.66 ->Bound: 0.22/0.66 2 0.22/0.66 ->Interpretation: 0.22/0.66 0.22/0.66 [a__U11](X) = 2.X + 2 0.22/0.66 [a__U12](X) = X 0.22/0.66 [a____](X1,X2) = 2.X1 + X2 + 2 0.22/0.66 [a__isNePal](X) = 2.X + 1 0.22/0.66 [mark](X) = X 0.22/0.66 [U11](X) = 2.X + 2 0.22/0.66 [U12](X) = X 0.22/0.66 [__](X1,X2) = 2.X1 + X2 + 2 0.22/0.66 [fSNonEmpty] = 0 0.22/0.66 [isNePal](X) = 2.X + 1 0.22/0.66 [nil] = 2 0.22/0.66 [tt] = 0 0.22/0.66 [A__U11](X) = 0 0.22/0.66 [A__U12](X) = 0 0.22/0.66 [A____](X1,X2) = 2.X1 + 2.X2 + 2 0.22/0.66 [A__ISNEPAL](X) = 0 0.22/0.66 [MARK](X) = 2.X + 1 0.22/0.66 0.22/0.66 Problem 1: 0.22/0.66 0.22/0.66 SCC Processor: 0.22/0.66 -> Pairs: 0.22/0.66 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 0.22/0.66 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 0.22/0.66 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 0.22/0.66 A____(nil,X:S) -> MARK(X:S) 0.22/0.66 A____(X:S,nil) -> MARK(X:S) 0.22/0.66 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.66 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.66 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.66 -> Rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 ->Strongly Connected Components: 0.22/0.66 ->->Cycle: 0.22/0.66 ->->-> Pairs: 0.22/0.66 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 0.22/0.66 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 0.22/0.66 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 0.22/0.66 A____(nil,X:S) -> MARK(X:S) 0.22/0.66 A____(X:S,nil) -> MARK(X:S) 0.22/0.66 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.66 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.66 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.66 ->->-> Rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 0.22/0.66 Problem 1: 0.22/0.66 0.22/0.66 Reduction Pairs Processor: 0.22/0.66 -> Pairs: 0.22/0.66 A____(__(X:S,Y:S),Z:S) -> MARK(X:S) 0.22/0.66 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 0.22/0.66 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 0.22/0.66 A____(nil,X:S) -> MARK(X:S) 0.22/0.66 A____(X:S,nil) -> MARK(X:S) 0.22/0.66 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.66 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.66 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.66 -> Rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 -> Usable rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 ->Interpretation type: 0.22/0.66 Linear 0.22/0.66 ->Coefficients: 0.22/0.66 Natural Numbers 0.22/0.66 ->Dimension: 0.22/0.66 1 0.22/0.66 ->Bound: 0.22/0.66 2 0.22/0.66 ->Interpretation: 0.22/0.66 0.22/0.66 [a__U11](X) = X + 2 0.22/0.66 [a__U12](X) = 2.X + 1 0.22/0.66 [a____](X1,X2) = 2.X1 + X2 + 2 0.22/0.66 [a__isNePal](X) = 2.X + 1 0.22/0.66 [mark](X) = X 0.22/0.66 [U11](X) = X + 2 0.22/0.66 [U12](X) = 2.X + 1 0.22/0.66 [__](X1,X2) = 2.X1 + X2 + 2 0.22/0.66 [fSNonEmpty] = 0 0.22/0.66 [isNePal](X) = 2.X + 1 0.22/0.66 [nil] = 0 0.22/0.66 [tt] = 1 0.22/0.66 [A__U11](X) = 0 0.22/0.66 [A__U12](X) = 0 0.22/0.66 [A____](X1,X2) = X1 + X2 + 2 0.22/0.66 [A__ISNEPAL](X) = 0 0.22/0.66 [MARK](X) = X + 1 0.22/0.66 0.22/0.66 Problem 1: 0.22/0.66 0.22/0.66 SCC Processor: 0.22/0.66 -> Pairs: 0.22/0.66 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 0.22/0.66 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 0.22/0.66 A____(nil,X:S) -> MARK(X:S) 0.22/0.66 A____(X:S,nil) -> MARK(X:S) 0.22/0.66 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.66 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.66 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.66 -> Rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 ->Strongly Connected Components: 0.22/0.66 ->->Cycle: 0.22/0.66 ->->-> Pairs: 0.22/0.66 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 0.22/0.66 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 0.22/0.66 A____(nil,X:S) -> MARK(X:S) 0.22/0.66 A____(X:S,nil) -> MARK(X:S) 0.22/0.66 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.66 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.66 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.66 ->->-> Rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 0.22/0.66 Problem 1: 0.22/0.66 0.22/0.66 Reduction Pairs Processor: 0.22/0.66 -> Pairs: 0.22/0.66 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S) 0.22/0.66 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 0.22/0.66 A____(nil,X:S) -> MARK(X:S) 0.22/0.66 A____(X:S,nil) -> MARK(X:S) 0.22/0.66 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.66 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.66 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.66 -> Rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 -> Usable rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 ->Interpretation type: 0.22/0.66 Linear 0.22/0.66 ->Coefficients: 0.22/0.66 Natural Numbers 0.22/0.66 ->Dimension: 0.22/0.66 1 0.22/0.66 ->Bound: 0.22/0.66 2 0.22/0.66 ->Interpretation: 0.22/0.66 0.22/0.66 [a__U11](X) = 2.X + 2 0.22/0.66 [a__U12](X) = 2.X + 2 0.22/0.66 [a____](X1,X2) = 2.X1 + X2 + 2 0.22/0.66 [a__isNePal](X) = 2.X + 2 0.22/0.66 [mark](X) = X 0.22/0.66 [U11](X) = 2.X + 2 0.22/0.66 [U12](X) = 2.X + 2 0.22/0.66 [__](X1,X2) = 2.X1 + X2 + 2 0.22/0.66 [fSNonEmpty] = 0 0.22/0.66 [isNePal](X) = 2.X + 2 0.22/0.66 [nil] = 2 0.22/0.66 [tt] = 2 0.22/0.66 [A__U11](X) = 0 0.22/0.66 [A__U12](X) = 0 0.22/0.66 [A____](X1,X2) = 2.X1 + 2.X2 + 2 0.22/0.66 [A__ISNEPAL](X) = 0 0.22/0.66 [MARK](X) = 2.X + 1 0.22/0.66 0.22/0.66 Problem 1: 0.22/0.66 0.22/0.66 SCC Processor: 0.22/0.66 -> Pairs: 0.22/0.66 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 0.22/0.66 A____(nil,X:S) -> MARK(X:S) 0.22/0.66 A____(X:S,nil) -> MARK(X:S) 0.22/0.66 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.66 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.66 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.66 -> Rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 ->Strongly Connected Components: 0.22/0.66 ->->Cycle: 0.22/0.66 ->->-> Pairs: 0.22/0.66 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 0.22/0.66 A____(nil,X:S) -> MARK(X:S) 0.22/0.66 A____(X:S,nil) -> MARK(X:S) 0.22/0.66 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.66 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.66 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.66 ->->-> Rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 0.22/0.66 Problem 1: 0.22/0.66 0.22/0.66 Reduction Pairs Processor: 0.22/0.66 -> Pairs: 0.22/0.66 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S) 0.22/0.66 A____(nil,X:S) -> MARK(X:S) 0.22/0.66 A____(X:S,nil) -> MARK(X:S) 0.22/0.66 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.66 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.66 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.66 -> Rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 -> Usable rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 ->Interpretation type: 0.22/0.66 Linear 0.22/0.66 ->Coefficients: 0.22/0.66 Natural Numbers 0.22/0.66 ->Dimension: 0.22/0.66 1 0.22/0.66 ->Bound: 0.22/0.66 2 0.22/0.66 ->Interpretation: 0.22/0.66 0.22/0.66 [a__U11](X) = 2.X + 1 0.22/0.66 [a__U12](X) = 2.X + 1 0.22/0.66 [a____](X1,X2) = 2.X1 + X2 + 2 0.22/0.66 [a__isNePal](X) = 2.X + 1 0.22/0.66 [mark](X) = X 0.22/0.66 [U11](X) = 2.X + 1 0.22/0.66 [U12](X) = 2.X + 1 0.22/0.66 [__](X1,X2) = 2.X1 + X2 + 2 0.22/0.66 [fSNonEmpty] = 0 0.22/0.66 [isNePal](X) = 2.X + 1 0.22/0.66 [nil] = 2 0.22/0.66 [tt] = 2 0.22/0.66 [A__U11](X) = 0 0.22/0.66 [A__U12](X) = 0 0.22/0.66 [A____](X1,X2) = 2.X1 + 2.X2 + 2 0.22/0.66 [A__ISNEPAL](X) = 0 0.22/0.66 [MARK](X) = 2.X + 2 0.22/0.66 0.22/0.66 Problem 1: 0.22/0.66 0.22/0.66 SCC Processor: 0.22/0.66 -> Pairs: 0.22/0.66 A____(nil,X:S) -> MARK(X:S) 0.22/0.66 A____(X:S,nil) -> MARK(X:S) 0.22/0.66 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.66 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.66 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.66 -> Rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 ->Strongly Connected Components: 0.22/0.66 ->->Cycle: 0.22/0.66 ->->-> Pairs: 0.22/0.66 A____(nil,X:S) -> MARK(X:S) 0.22/0.66 A____(X:S,nil) -> MARK(X:S) 0.22/0.66 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.66 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.66 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.66 ->->-> Rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 0.22/0.66 Problem 1: 0.22/0.66 0.22/0.66 Reduction Pairs Processor: 0.22/0.66 -> Pairs: 0.22/0.66 A____(nil,X:S) -> MARK(X:S) 0.22/0.66 A____(X:S,nil) -> MARK(X:S) 0.22/0.66 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.66 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.66 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.66 -> Rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 -> Usable rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 ->Interpretation type: 0.22/0.66 Linear 0.22/0.66 ->Coefficients: 0.22/0.66 Natural Numbers 0.22/0.66 ->Dimension: 0.22/0.66 1 0.22/0.66 ->Bound: 0.22/0.66 2 0.22/0.66 ->Interpretation: 0.22/0.66 0.22/0.66 [a__U11](X) = 2.X + 2 0.22/0.66 [a__U12](X) = X + 2 0.22/0.66 [a____](X1,X2) = 2.X1 + X2 + 2 0.22/0.66 [a__isNePal](X) = 2.X 0.22/0.66 [mark](X) = X 0.22/0.66 [U11](X) = 2.X + 2 0.22/0.66 [U12](X) = X + 2 0.22/0.66 [__](X1,X2) = 2.X1 + X2 + 2 0.22/0.66 [fSNonEmpty] = 0 0.22/0.66 [isNePal](X) = 2.X 0.22/0.66 [nil] = 2 0.22/0.66 [tt] = 2 0.22/0.66 [A__U11](X) = 0 0.22/0.66 [A__U12](X) = 0 0.22/0.66 [A____](X1,X2) = 2.X1 + 2.X2 + 2 0.22/0.66 [A__ISNEPAL](X) = 0 0.22/0.66 [MARK](X) = 2.X + 2 0.22/0.66 0.22/0.66 Problem 1: 0.22/0.66 0.22/0.66 SCC Processor: 0.22/0.66 -> Pairs: 0.22/0.66 A____(X:S,nil) -> MARK(X:S) 0.22/0.66 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.66 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.66 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.66 -> Rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 ->Strongly Connected Components: 0.22/0.66 ->->Cycle: 0.22/0.66 ->->-> Pairs: 0.22/0.66 A____(X:S,nil) -> MARK(X:S) 0.22/0.66 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.66 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.66 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.66 ->->-> Rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 0.22/0.66 Problem 1: 0.22/0.66 0.22/0.66 Reduction Pairs Processor: 0.22/0.66 -> Pairs: 0.22/0.66 A____(X:S,nil) -> MARK(X:S) 0.22/0.66 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.66 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.66 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.66 -> Rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 -> Usable rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 ->Interpretation type: 0.22/0.66 Linear 0.22/0.66 ->Coefficients: 0.22/0.66 Natural Numbers 0.22/0.66 ->Dimension: 0.22/0.66 1 0.22/0.66 ->Bound: 0.22/0.66 2 0.22/0.66 ->Interpretation: 0.22/0.66 0.22/0.66 [a__U11](X) = 2.X + 2 0.22/0.66 [a__U12](X) = X + 2 0.22/0.66 [a____](X1,X2) = 2.X1 + X2 + 2 0.22/0.66 [a__isNePal](X) = 2.X + 1 0.22/0.66 [mark](X) = X 0.22/0.66 [U11](X) = 2.X + 2 0.22/0.66 [U12](X) = X + 2 0.22/0.66 [__](X1,X2) = 2.X1 + X2 + 2 0.22/0.66 [fSNonEmpty] = 0 0.22/0.66 [isNePal](X) = 2.X + 1 0.22/0.66 [nil] = 0 0.22/0.66 [tt] = 2 0.22/0.66 [A__U11](X) = 0 0.22/0.66 [A__U12](X) = 0 0.22/0.66 [A____](X1,X2) = 2.X1 + 2 0.22/0.66 [A__ISNEPAL](X) = 0 0.22/0.66 [MARK](X) = 2.X + 1 0.22/0.66 0.22/0.66 Problem 1: 0.22/0.66 0.22/0.66 SCC Processor: 0.22/0.66 -> Pairs: 0.22/0.66 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.66 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S)) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.66 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.66 -> Rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 ->Strongly Connected Components: 0.22/0.66 ->->Cycle: 0.22/0.66 ->->-> Pairs: 0.22/0.66 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.66 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.66 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.66 ->->-> Rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 0.22/0.66 Problem 1: 0.22/0.66 0.22/0.66 Subterm Processor: 0.22/0.66 -> Pairs: 0.22/0.66 MARK(U11(X:S)) -> MARK(X:S) 0.22/0.66 MARK(U12(X:S)) -> MARK(X:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X1:S) 0.22/0.66 MARK(__(X1:S,X2:S)) -> MARK(X2:S) 0.22/0.66 MARK(isNePal(X:S)) -> MARK(X:S) 0.22/0.66 -> Rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 ->Projection: 0.22/0.66 pi(MARK) = 1 0.22/0.66 0.22/0.66 Problem 1: 0.22/0.66 0.22/0.66 SCC Processor: 0.22/0.66 -> Pairs: 0.22/0.66 Empty 0.22/0.66 -> Rules: 0.22/0.66 a__U11(tt) -> a__U12(tt) 0.22/0.66 a__U11(X:S) -> U11(X:S) 0.22/0.66 a__U12(tt) -> tt 0.22/0.66 a__U12(X:S) -> U12(X:S) 0.22/0.66 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S))) 0.22/0.66 a____(nil,X:S) -> mark(X:S) 0.22/0.66 a____(X:S,nil) -> mark(X:S) 0.22/0.66 a____(X1:S,X2:S) -> __(X1:S,X2:S) 0.22/0.66 a__isNePal(__(I:S,__(P:S,I:S))) -> a__U11(tt) 0.22/0.66 a__isNePal(X:S) -> isNePal(X:S) 0.22/0.66 mark(U11(X:S)) -> a__U11(mark(X:S)) 0.22/0.66 mark(U12(X:S)) -> a__U12(mark(X:S)) 0.22/0.66 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S)) 0.22/0.66 mark(isNePal(X:S)) -> a__isNePal(mark(X:S)) 0.22/0.66 mark(nil) -> nil 0.22/0.66 mark(tt) -> tt 0.22/0.66 ->Strongly Connected Components: 0.22/0.66 There is no strongly connected component 0.22/0.66 0.22/0.66 The problem is finite. 0.22/0.66 EOF