YES

Problem 1: 

(VAR v_NonEmpty:S I:S P:S X:S X1:S X2:S Y:S Z:S)
(RULES
a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
a____(nil,X:S) -> mark(X:S)
a____(X:S,nil) -> mark(X:S)
a____(X1:S,X2:S) -> __(X1:S,X2:S)
a__and(tt,X:S) -> mark(X:S)
a__and(X1:S,X2:S) -> and(X1:S,X2:S)
a__isNePal(__(I:S,__(P:S,I:S))) -> tt
a__isNePal(X:S) -> isNePal(X:S)
mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
mark(nil) -> nil
mark(tt) -> tt
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S))
 A____(__(X:S,Y:S),Z:S) -> MARK(X:S)
 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
 A____(nil,X:S) -> MARK(X:S)
 A____(X:S,nil) -> MARK(X:S)
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> A__ISNEPAL(mark(X:S))
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt

Problem 1: 

SCC Processor:
-> Pairs:
 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S))
 A____(__(X:S,Y:S),Z:S) -> MARK(X:S)
 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
 A____(nil,X:S) -> MARK(X:S)
 A____(X:S,nil) -> MARK(X:S)
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> A__ISNEPAL(mark(X:S))
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S))
 A____(__(X:S,Y:S),Z:S) -> MARK(X:S)
 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
 A____(nil,X:S) -> MARK(X:S)
 A____(X:S,nil) -> MARK(X:S)
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
->->-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A____(__(X:S,Y:S),Z:S) -> A____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S))
 A____(__(X:S,Y:S),Z:S) -> MARK(X:S)
 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
 A____(nil,X:S) -> MARK(X:S)
 A____(X:S,nil) -> MARK(X:S)
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
-> Usable rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a____](X1,X2) = 2.X1 + X2 + 1
[a__and](X1,X2) = 2.X1 + 2.X2 + 1
[a__isNePal](X) = 2.X + 1
[mark](X) = X
[__](X1,X2) = 2.X1 + X2 + 1
[and](X1,X2) = 2.X1 + 2.X2 + 1
[fSNonEmpty] = 0
[isNePal](X) = 2.X + 1
[nil] = 0
[tt] = 1
[A____](X1,X2) = 2.X1 + X2 + 2
[A__AND](X1,X2) = 2.X1 + 2.X2 + 1
[A__ISNEPAL](X) = 0
[MARK](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S))
 A____(__(X:S,Y:S),Z:S) -> MARK(X:S)
 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
 A____(nil,X:S) -> MARK(X:S)
 A____(X:S,nil) -> MARK(X:S)
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S))
 A____(__(X:S,Y:S),Z:S) -> MARK(X:S)
 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
 A____(nil,X:S) -> MARK(X:S)
 A____(X:S,nil) -> MARK(X:S)
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
->->-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A____(__(X:S,Y:S),Z:S) -> A____(mark(Y:S),mark(Z:S))
 A____(__(X:S,Y:S),Z:S) -> MARK(X:S)
 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
 A____(nil,X:S) -> MARK(X:S)
 A____(X:S,nil) -> MARK(X:S)
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
-> Usable rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a____](X1,X2) = 2.X1 + X2 + 2
[a__and](X1,X2) = 2.X1 + 2.X2 + 2
[a__isNePal](X) = 2.X + 2
[mark](X) = X
[__](X1,X2) = 2.X1 + X2 + 2
[and](X1,X2) = 2.X1 + 2.X2 + 2
[fSNonEmpty] = 0
[isNePal](X) = 2.X + 2
[nil] = 0
[tt] = 1
[A____](X1,X2) = 2.X1 + 2.X2 + 2
[A__AND](X1,X2) = 2.X1 + 2.X2 + 2
[A__ISNEPAL](X) = 0
[MARK](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 A____(__(X:S,Y:S),Z:S) -> MARK(X:S)
 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
 A____(nil,X:S) -> MARK(X:S)
 A____(X:S,nil) -> MARK(X:S)
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A____(__(X:S,Y:S),Z:S) -> MARK(X:S)
 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
 A____(nil,X:S) -> MARK(X:S)
 A____(X:S,nil) -> MARK(X:S)
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
->->-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A____(__(X:S,Y:S),Z:S) -> MARK(X:S)
 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
 A____(nil,X:S) -> MARK(X:S)
 A____(X:S,nil) -> MARK(X:S)
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
-> Usable rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a____](X1,X2) = 2.X1 + X2 + 1
[a__and](X1,X2) = 2.X1 + 2.X2 + 2
[a__isNePal](X) = 2.X + 1
[mark](X) = X
[__](X1,X2) = 2.X1 + X2 + 1
[and](X1,X2) = 2.X1 + 2.X2 + 2
[fSNonEmpty] = 0
[isNePal](X) = 2.X + 1
[nil] = 2
[tt] = 2
[A____](X1,X2) = 2.X1 + 2.X2 + 1
[A__AND](X1,X2) = X1 + 2.X2 + 2
[A__ISNEPAL](X) = 0
[MARK](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
 A____(nil,X:S) -> MARK(X:S)
 A____(X:S,nil) -> MARK(X:S)
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
 A____(nil,X:S) -> MARK(X:S)
 A____(X:S,nil) -> MARK(X:S)
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
->->-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A____(__(X:S,Y:S),Z:S) -> MARK(Y:S)
 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
 A____(nil,X:S) -> MARK(X:S)
 A____(X:S,nil) -> MARK(X:S)
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
-> Usable rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a____](X1,X2) = 2.X1 + X2 + 2
[a__and](X1,X2) = 2.X1 + X2 + 1
[a__isNePal](X) = X + 1
[mark](X) = X
[__](X1,X2) = 2.X1 + X2 + 2
[and](X1,X2) = 2.X1 + X2 + 1
[fSNonEmpty] = 0
[isNePal](X) = X + 1
[nil] = 1
[tt] = 1
[A____](X1,X2) = 2.X1 + 2.X2
[A__AND](X1,X2) = 2.X1 + 2.X2 + 2
[A__ISNEPAL](X) = 0
[MARK](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
 A____(nil,X:S) -> MARK(X:S)
 A____(X:S,nil) -> MARK(X:S)
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
 A____(nil,X:S) -> MARK(X:S)
 A____(X:S,nil) -> MARK(X:S)
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
->->-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A____(__(X:S,Y:S),Z:S) -> MARK(Z:S)
 A____(nil,X:S) -> MARK(X:S)
 A____(X:S,nil) -> MARK(X:S)
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
-> Usable rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a____](X1,X2) = 2.X1 + X2 + 2
[a__and](X1,X2) = 2.X1 + 2.X2 + 2
[a__isNePal](X) = X + 2
[mark](X) = X
[__](X1,X2) = 2.X1 + X2 + 2
[and](X1,X2) = 2.X1 + 2.X2 + 2
[fSNonEmpty] = 0
[isNePal](X) = X + 2
[nil] = 2
[tt] = 0
[A____](X1,X2) = 2.X1 + 2.X2 + 2
[A__AND](X1,X2) = 2.X1 + 2.X2 + 2
[A__ISNEPAL](X) = 0
[MARK](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 A____(nil,X:S) -> MARK(X:S)
 A____(X:S,nil) -> MARK(X:S)
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A____(nil,X:S) -> MARK(X:S)
 A____(X:S,nil) -> MARK(X:S)
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
->->-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A____(nil,X:S) -> MARK(X:S)
 A____(X:S,nil) -> MARK(X:S)
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
-> Usable rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a____](X1,X2) = 2.X1 + X2 + 2
[a__and](X1,X2) = X1 + 2.X2 + 2
[a__isNePal](X) = 2.X + 1
[mark](X) = X
[__](X1,X2) = 2.X1 + X2 + 2
[and](X1,X2) = X1 + 2.X2 + 2
[fSNonEmpty] = 0
[isNePal](X) = 2.X + 1
[nil] = 2
[tt] = 0
[A____](X1,X2) = 2.X1 + 2.X2 + 2
[A__AND](X1,X2) = 2.X2 + 2
[A__ISNEPAL](X) = 0
[MARK](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 A____(X:S,nil) -> MARK(X:S)
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A____(X:S,nil) -> MARK(X:S)
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
->->-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A____(X:S,nil) -> MARK(X:S)
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
-> Usable rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a____](X1,X2) = 2.X1 + X2 + 2
[a__and](X1,X2) = X1 + 2.X2 + 2
[a__isNePal](X) = 2.X
[mark](X) = X
[__](X1,X2) = 2.X1 + X2 + 2
[and](X1,X2) = X1 + 2.X2 + 2
[fSNonEmpty] = 0
[isNePal](X) = 2.X
[nil] = 2
[tt] = 2
[A____](X1,X2) = 2.X1 + X2
[A__AND](X1,X2) = 2.X1 + 2.X2 + 1
[A__ISNEPAL](X) = 0
[MARK](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> A____(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
->->-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt

Problem 1: 

Subterm Processor:
-> Pairs:
 A__AND(tt,X:S) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(and(X1:S,X2:S)) -> A__AND(mark(X1:S),X2:S)
 MARK(and(X1:S,X2:S)) -> MARK(X1:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
->Projection:
 pi(A__AND) = 2
 pi(MARK) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 A__AND(tt,X:S) -> MARK(X:S)
-> Rules:
 a____(__(X:S,Y:S),Z:S) -> a____(mark(X:S),a____(mark(Y:S),mark(Z:S)))
 a____(nil,X:S) -> mark(X:S)
 a____(X:S,nil) -> mark(X:S)
 a____(X1:S,X2:S) -> __(X1:S,X2:S)
 a__and(tt,X:S) -> mark(X:S)
 a__and(X1:S,X2:S) -> and(X1:S,X2:S)
 a__isNePal(__(I:S,__(P:S,I:S))) -> tt
 a__isNePal(X:S) -> isNePal(X:S)
 mark(__(X1:S,X2:S)) -> a____(mark(X1:S),mark(X2:S))
 mark(and(X1:S,X2:S)) -> a__and(mark(X1:S),X2:S)
 mark(isNePal(X:S)) -> a__isNePal(mark(X:S))
 mark(nil) -> nil
 mark(tt) -> tt
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.