YES

Problem 1: 

(VAR v_NonEmpty:S I:S P:S X:S X1:S X2:S Y:S Z:S)
(RULES
U11(active(X:S)) -> U11(X:S)
U11(mark(X:S)) -> U11(X:S)
U12(active(X:S)) -> U12(X:S)
U12(mark(X:S)) -> U12(X:S)
__(active(X1:S),X2:S) -> __(X1:S,X2:S)
__(mark(X1:S),X2:S) -> __(X1:S,X2:S)
__(X1:S,active(X2:S)) -> __(X1:S,X2:S)
__(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
active(U11(tt)) -> mark(U12(tt))
active(U12(tt)) -> mark(tt)
active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
active(__(nil,X:S)) -> mark(X:S)
active(__(X:S,nil)) -> mark(X:S)
active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
isNePal(active(X:S)) -> isNePal(X:S)
isNePal(mark(X:S)) -> isNePal(X:S)
mark(U11(X:S)) -> active(U11(mark(X:S)))
mark(U12(X:S)) -> active(U12(mark(X:S)))
mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
mark(nil) -> active(nil)
mark(tt) -> active(tt)
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 U11#(active(X:S)) -> U11#(X:S)
 U11#(mark(X:S)) -> U11#(X:S)
 U12#(active(X:S)) -> U12#(X:S)
 U12#(mark(X:S)) -> U12#(X:S)
 __#(active(X1:S),X2:S) -> __#(X1:S,X2:S)
 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S)
 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S)
 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
 ACTIVE(U11(tt)) -> MARK(U12(tt))
 ACTIVE(U12(tt)) -> MARK(tt)
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(X:S,__(Y:S,Z:S))
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(Y:S,Z:S)
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U11(tt))
 ISNEPAL(active(X:S)) -> ISNEPAL(X:S)
 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S)
 MARK(U11(X:S)) -> U11#(mark(X:S))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U12(X:S)) -> U12#(mark(X:S))
 MARK(U12(X:S)) -> ACTIVE(U12(mark(X:S)))
 MARK(U12(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> __#(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S)))
 MARK(isNePal(X:S)) -> ISNEPAL(mark(X:S))
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)

Problem 1: 

SCC Processor:
-> Pairs:
 U11#(active(X:S)) -> U11#(X:S)
 U11#(mark(X:S)) -> U11#(X:S)
 U12#(active(X:S)) -> U12#(X:S)
 U12#(mark(X:S)) -> U12#(X:S)
 __#(active(X1:S),X2:S) -> __#(X1:S,X2:S)
 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S)
 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S)
 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
 ACTIVE(U11(tt)) -> MARK(U12(tt))
 ACTIVE(U12(tt)) -> MARK(tt)
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(X:S,__(Y:S,Z:S))
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> __#(Y:S,Z:S)
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U11(tt))
 ISNEPAL(active(X:S)) -> ISNEPAL(X:S)
 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S)
 MARK(U11(X:S)) -> U11#(mark(X:S))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U12(X:S)) -> U12#(mark(X:S))
 MARK(U12(X:S)) -> ACTIVE(U12(mark(X:S)))
 MARK(U12(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> __#(mark(X1:S),mark(X2:S))
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S)))
 MARK(isNePal(X:S)) -> ISNEPAL(mark(X:S))
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ISNEPAL(active(X:S)) -> ISNEPAL(X:S)
 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->->Cycle:
->->-> Pairs:
 __#(active(X1:S),X2:S) -> __#(X1:S,X2:S)
 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S)
 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S)
 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->->Cycle:
->->-> Pairs:
 U12#(active(X:S)) -> U12#(X:S)
 U12#(mark(X:S)) -> U12#(X:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->->Cycle:
->->-> Pairs:
 U11#(active(X:S)) -> U11#(X:S)
 U11#(mark(X:S)) -> U11#(X:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->->Cycle:
->->-> Pairs:
 ACTIVE(U11(tt)) -> MARK(U12(tt))
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U11(tt))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U12(X:S)) -> ACTIVE(U12(mark(X:S)))
 MARK(U12(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S)))
 MARK(isNePal(X:S)) -> MARK(X:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)


The problem is decomposed in 5 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 ISNEPAL(active(X:S)) -> ISNEPAL(X:S)
 ISNEPAL(mark(X:S)) -> ISNEPAL(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Projection:
 pi(ISNEPAL) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 __#(active(X1:S),X2:S) -> __#(X1:S,X2:S)
 __#(mark(X1:S),X2:S) -> __#(X1:S,X2:S)
 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S)
 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Projection:
 pi(__#) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S)
 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S)
 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)

Problem 1.2: 

Subterm Processor:
-> Pairs:
 __#(X1:S,active(X2:S)) -> __#(X1:S,X2:S)
 __#(X1:S,mark(X2:S)) -> __#(X1:S,X2:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Projection:
 pi(__#) = 2

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.3: 

Subterm Processor:
-> Pairs:
 U12#(active(X:S)) -> U12#(X:S)
 U12#(mark(X:S)) -> U12#(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Projection:
 pi(U12#) = 1

Problem 1.3: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.4: 

Subterm Processor:
-> Pairs:
 U11#(active(X:S)) -> U11#(X:S)
 U11#(mark(X:S)) -> U11#(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Projection:
 pi(U11#) = 1

Problem 1.4: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.5: 

Reduction Pairs Processor:
-> Pairs:
 ACTIVE(U11(tt)) -> MARK(U12(tt))
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U11(tt))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U12(X:S)) -> ACTIVE(U12(mark(X:S)))
 MARK(U12(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S)))
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
-> Usable rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[U11](X) = 2.X + 2
[U12](X) = X + 2
[__](X1,X2) = 2.X1 + X2 + 2
[active](X) = X
[isNePal](X) = 2.X + 2
[mark](X) = X
[fSNonEmpty] = 0
[nil] = 1
[tt] = 2
[U11#](X) = 0
[U12#](X) = 0
[__#](X1,X2) = 0
[ACTIVE](X) = 2.X + 1
[ISNEPAL](X) = 0
[MARK](X) = 2.X + 2

Problem 1.5: 

SCC Processor:
-> Pairs:
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U11(tt))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U12(X:S)) -> ACTIVE(U12(mark(X:S)))
 MARK(U12(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S)))
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U11(tt))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U12(X:S)) -> ACTIVE(U12(mark(X:S)))
 MARK(U12(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S)))
 MARK(isNePal(X:S)) -> MARK(X:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)

Problem 1.5: 

Reduction Pairs Processor:
-> Pairs:
 ACTIVE(__(__(X:S,Y:S),Z:S)) -> MARK(__(X:S,__(Y:S,Z:S)))
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U11(tt))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U12(X:S)) -> ACTIVE(U12(mark(X:S)))
 MARK(U12(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S)))
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
-> Usable rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[U11](X) = 2.X + 2
[U12](X) = 2.X + 2
[__](X1,X2) = 2.X1 + X2 + 2
[active](X) = X
[isNePal](X) = 2.X + 2
[mark](X) = X
[fSNonEmpty] = 0
[nil] = 2
[tt] = 2
[U11#](X) = 0
[U12#](X) = 0
[__#](X1,X2) = 0
[ACTIVE](X) = 2.X
[ISNEPAL](X) = 0
[MARK](X) = 2.X + 2

Problem 1.5: 

SCC Processor:
-> Pairs:
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U11(tt))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U12(X:S)) -> ACTIVE(U12(mark(X:S)))
 MARK(U12(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S)))
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U11(tt))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U12(X:S)) -> ACTIVE(U12(mark(X:S)))
 MARK(U12(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S)))
 MARK(isNePal(X:S)) -> MARK(X:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)

Problem 1.5: 

Reduction Pairs Processor:
-> Pairs:
 ACTIVE(__(nil,X:S)) -> MARK(X:S)
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U11(tt))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U12(X:S)) -> ACTIVE(U12(mark(X:S)))
 MARK(U12(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S)))
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
-> Usable rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[U11](X) = 2.X + 2
[U12](X) = X + 2
[__](X1,X2) = 2.X1 + X2 + 2
[active](X) = X
[isNePal](X) = 2.X + 1
[mark](X) = X
[fSNonEmpty] = 0
[nil] = 2
[tt] = 0
[U11#](X) = 0
[U12#](X) = 0
[__#](X1,X2) = 0
[ACTIVE](X) = 2.X + 2
[ISNEPAL](X) = 0
[MARK](X) = 2.X + 2

Problem 1.5: 

SCC Processor:
-> Pairs:
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U11(tt))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U12(X:S)) -> ACTIVE(U12(mark(X:S)))
 MARK(U12(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S)))
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U11(tt))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U12(X:S)) -> ACTIVE(U12(mark(X:S)))
 MARK(U12(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S)))
 MARK(isNePal(X:S)) -> MARK(X:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)

Problem 1.5: 

Reduction Pairs Processor:
-> Pairs:
 ACTIVE(__(X:S,nil)) -> MARK(X:S)
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U11(tt))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U12(X:S)) -> ACTIVE(U12(mark(X:S)))
 MARK(U12(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S)))
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
-> Usable rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[U11](X) = 2.X + 2
[U12](X) = X + 1
[__](X1,X2) = 2.X1 + X2 + 2
[active](X) = X
[isNePal](X) = 2.X + 2
[mark](X) = X
[fSNonEmpty] = 0
[nil] = 1
[tt] = 2
[U11#](X) = 0
[U12#](X) = 0
[__#](X1,X2) = 0
[ACTIVE](X) = 2.X + 1
[ISNEPAL](X) = 0
[MARK](X) = 2.X + 2

Problem 1.5: 

SCC Processor:
-> Pairs:
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U11(tt))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U12(X:S)) -> ACTIVE(U12(mark(X:S)))
 MARK(U12(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S)))
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U11(tt))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U12(X:S)) -> ACTIVE(U12(mark(X:S)))
 MARK(U12(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S)))
 MARK(isNePal(X:S)) -> MARK(X:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)

Problem 1.5: 

Reduction Pairs Processor:
-> Pairs:
 ACTIVE(isNePal(__(I:S,__(P:S,I:S)))) -> MARK(U11(tt))
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U12(X:S)) -> ACTIVE(U12(mark(X:S)))
 MARK(U12(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S)))
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
-> Usable rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[U11](X) = 2.X + 1
[U12](X) = 2.X
[__](X1,X2) = 2.X1 + X2
[active](X) = X
[isNePal](X) = 2.X + 2
[mark](X) = X
[fSNonEmpty] = 0
[nil] = 2
[tt] = 0
[U11#](X) = 0
[U12#](X) = 0
[__#](X1,X2) = 0
[ACTIVE](X) = 2.X + 2
[ISNEPAL](X) = 0
[MARK](X) = 2.X + 2

Problem 1.5: 

SCC Processor:
-> Pairs:
 MARK(U11(X:S)) -> ACTIVE(U11(mark(X:S)))
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U12(X:S)) -> ACTIVE(U12(mark(X:S)))
 MARK(U12(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> ACTIVE(__(mark(X1:S),mark(X2:S)))
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> ACTIVE(isNePal(mark(X:S)))
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U12(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
->->-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)

Problem 1.5: 

Subterm Processor:
-> Pairs:
 MARK(U11(X:S)) -> MARK(X:S)
 MARK(U12(X:S)) -> MARK(X:S)
 MARK(__(X1:S,X2:S)) -> MARK(X1:S)
 MARK(__(X1:S,X2:S)) -> MARK(X2:S)
 MARK(isNePal(X:S)) -> MARK(X:S)
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Projection:
 pi(MARK) = 1

Problem 1.5: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 U11(active(X:S)) -> U11(X:S)
 U11(mark(X:S)) -> U11(X:S)
 U12(active(X:S)) -> U12(X:S)
 U12(mark(X:S)) -> U12(X:S)
 __(active(X1:S),X2:S) -> __(X1:S,X2:S)
 __(mark(X1:S),X2:S) -> __(X1:S,X2:S)
 __(X1:S,active(X2:S)) -> __(X1:S,X2:S)
 __(X1:S,mark(X2:S)) -> __(X1:S,X2:S)
 active(U11(tt)) -> mark(U12(tt))
 active(U12(tt)) -> mark(tt)
 active(__(__(X:S,Y:S),Z:S)) -> mark(__(X:S,__(Y:S,Z:S)))
 active(__(nil,X:S)) -> mark(X:S)
 active(__(X:S,nil)) -> mark(X:S)
 active(isNePal(__(I:S,__(P:S,I:S)))) -> mark(U11(tt))
 isNePal(active(X:S)) -> isNePal(X:S)
 isNePal(mark(X:S)) -> isNePal(X:S)
 mark(U11(X:S)) -> active(U11(mark(X:S)))
 mark(U12(X:S)) -> active(U12(mark(X:S)))
 mark(__(X1:S,X2:S)) -> active(__(mark(X1:S),mark(X2:S)))
 mark(isNePal(X:S)) -> active(isNePal(mark(X:S)))
 mark(nil) -> active(nil)
 mark(tt) -> active(tt)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.