YES

Problem:
 __(__(X,Y),Z) -> __(X,__(Y,Z))
 __(X,nil()) -> X
 __(nil(),X) -> X
 U11(tt()) -> U12(tt())
 U12(tt()) -> tt()
 isNePal(__(I,__(P,I))) -> U11(tt())
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   __#(__(X,Y),Z) -> __#(Y,Z)
   __#(__(X,Y),Z) -> __#(X,__(Y,Z))
   U11#(tt()) -> U12#(tt())
   isNePal#(__(I,__(P,I))) -> U11#(tt())
  TRS:
   __(__(X,Y),Z) -> __(X,__(Y,Z))
   __(X,nil()) -> X
   __(nil(),X) -> X
   U11(tt()) -> U12(tt())
   U12(tt()) -> tt()
   isNePal(__(I,__(P,I))) -> U11(tt())
   activate(X) -> X
  Usable Rule Processor:
   DPs:
    __#(__(X,Y),Z) -> __#(Y,Z)
    __#(__(X,Y),Z) -> __#(X,__(Y,Z))
    U11#(tt()) -> U12#(tt())
    isNePal#(__(I,__(P,I))) -> U11#(tt())
   TRS:
    __(__(X,Y),Z) -> __(X,__(Y,Z))
    __(X,nil()) -> X
    __(nil(),X) -> X
   Matrix Interpretation Processor: dim=1
    
    usable rules:
     __(__(X,Y),Z) -> __(X,__(Y,Z))
     __(X,nil()) -> X
     __(nil(),X) -> X
    interpretation:
     [isNePal#](x0) = 3x0 + 1,
     
     [U12#](x0) = 2x0,
     
     [U11#](x0) = 2x0 + 2,
     
     [__#](x0, x1) = x0 + 2,
     
     [tt] = 2,
     
     [nil] = 0,
     
     [__](x0, x1) = x0 + x1 + 1
    orientation:
     __#(__(X,Y),Z) = X + Y + 3 >= Y + 2 = __#(Y,Z)
     
     __#(__(X,Y),Z) = X + Y + 3 >= X + 2 = __#(X,__(Y,Z))
     
     U11#(tt()) = 6 >= 4 = U12#(tt())
     
     isNePal#(__(I,__(P,I))) = 6I + 3P + 7 >= 6 = U11#(tt())
     
     __(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = __(X,__(Y,Z))
     
     __(X,nil()) = X + 1 >= X = X
     
     __(nil(),X) = X + 1 >= X = X
    problem:
     DPs:
      
     TRS:
      __(__(X,Y),Z) -> __(X,__(Y,Z))
      __(X,nil()) -> X
      __(nil(),X) -> X
    Qed