YES

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

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