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
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [isNePal#](x0) = 3x0 + 5/2,
    
    [U12#](x0) = 3x0,
    
    [U11#](x0) = 5/2x0 + 3,
    
    [__#](x0, x1) = 5/2x0 + x1 + 1,
    
    [activate](x0) = x0,
    
    [isNePal](x0) = x0 + 1,
    
    [U12](x0) = x0,
    
    [U11](x0) = 2,
    
    [tt] = 2,
    
    [nil] = 1/2,
    
    [__](x0, x1) = x0 + x1 + 1
   orientation:
    __#(__(X,Y),Z) = 5/2X + 5/2Y + Z + 7/2 >= 5/2Y + Z + 1 = __#(Y,Z)
    
    __#(__(X,Y),Z) = 5/2X + 5/2Y + Z + 7/2 >= 5/2X + Y + Z + 2 = __#(X,__(Y,Z))
    
    U11#(tt()) = 8 >= 6 = U12#(tt())
    
    isNePal#(__(I,__(P,I))) = 6I + 3P + 17/2 >= 8 = U11#(tt())
    
    __(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = __(X,__(Y,Z))
    
    __(X,nil()) = X + 3/2 >= X = X
    
    __(nil(),X) = X + 3/2 >= X = X
    
    U11(tt()) = 2 >= 2 = U12(tt())
    
    U12(tt()) = 2 >= 2 = tt()
    
    isNePal(__(I,__(P,I))) = 2I + P + 3 >= 2 = U11(tt())
    
    activate(X) = X >= X = X
   problem:
    DPs:
     
    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
   Qed