YES

Problem:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(X,nil()) -> mark(X)
 a____(nil(),X) -> mark(X)
 a__U11(tt()) -> a__U12(tt())
 a__U12(tt()) -> tt()
 a__isNePal(__(I,__(P,I))) -> a__U11(tt())
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(U11(X)) -> a__U11(mark(X))
 mark(U12(X)) -> a__U12(mark(X))
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil()) -> nil()
 mark(tt()) -> tt()
 a____(X1,X2) -> __(X1,X2)
 a__U11(X) -> U11(X)
 a__U12(X) -> U12(X)
 a__isNePal(X) -> isNePal(X)

Proof:
 DP Processor:
  DPs:
   a____#(__(X,Y),Z) -> mark#(Z)
   a____#(__(X,Y),Z) -> mark#(Y)
   a____#(__(X,Y),Z) -> a____#(mark(Y),mark(Z))
   a____#(__(X,Y),Z) -> mark#(X)
   a____#(__(X,Y),Z) -> a____#(mark(X),a____(mark(Y),mark(Z)))
   a____#(X,nil()) -> mark#(X)
   a____#(nil(),X) -> mark#(X)
   a__U11#(tt()) -> a__U12#(tt())
   a__isNePal#(__(I,__(P,I))) -> a__U11#(tt())
   mark#(__(X1,X2)) -> mark#(X2)
   mark#(__(X1,X2)) -> mark#(X1)
   mark#(__(X1,X2)) -> a____#(mark(X1),mark(X2))
   mark#(U11(X)) -> mark#(X)
   mark#(U11(X)) -> a__U11#(mark(X))
   mark#(U12(X)) -> mark#(X)
   mark#(U12(X)) -> a__U12#(mark(X))
   mark#(isNePal(X)) -> mark#(X)
   mark#(isNePal(X)) -> a__isNePal#(mark(X))
  TRS:
   a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
   a____(X,nil()) -> mark(X)
   a____(nil(),X) -> mark(X)
   a__U11(tt()) -> a__U12(tt())
   a__U12(tt()) -> tt()
   a__isNePal(__(I,__(P,I))) -> a__U11(tt())
   mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
   mark(U11(X)) -> a__U11(mark(X))
   mark(U12(X)) -> a__U12(mark(X))
   mark(isNePal(X)) -> a__isNePal(mark(X))
   mark(nil()) -> nil()
   mark(tt()) -> tt()
   a____(X1,X2) -> __(X1,X2)
   a__U11(X) -> U11(X)
   a__U12(X) -> U12(X)
   a__isNePal(X) -> isNePal(X)
  Matrix Interpretation Processor: dim=1
   
   usable rules:
    a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
    a____(X,nil()) -> mark(X)
    a____(nil(),X) -> mark(X)
    a__U11(tt()) -> a__U12(tt())
    a__U12(tt()) -> tt()
    a__isNePal(__(I,__(P,I))) -> a__U11(tt())
    mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
    mark(U11(X)) -> a__U11(mark(X))
    mark(U12(X)) -> a__U12(mark(X))
    mark(isNePal(X)) -> a__isNePal(mark(X))
    mark(nil()) -> nil()
    mark(tt()) -> tt()
    a____(X1,X2) -> __(X1,X2)
    a__U11(X) -> U11(X)
    a__U12(X) -> U12(X)
    a__isNePal(X) -> isNePal(X)
   interpretation:
    [a__isNePal#](x0) = x0 + 5,
    
    [a__U12#](x0) = x0 + 3,
    
    [a__U11#](x0) = x0 + 4,
    
    [mark#](x0) = 2x0 + 1,
    
    [a____#](x0, x1) = 4x0 + 2x1,
    
    [isNePal](x0) = x0 + 5,
    
    [U12](x0) = 2x0 + 2,
    
    [U11](x0) = 5x0 + 2,
    
    [a__isNePal](x0) = x0 + 5,
    
    [a__U12](x0) = 2x0 + 2,
    
    [a__U11](x0) = 5x0 + 2,
    
    [tt] = 1,
    
    [nil] = 2,
    
    [mark](x0) = x0,
    
    [a____](x0, x1) = 2x0 + x1 + 1,
    
    [__](x0, x1) = 2x0 + x1 + 1
   orientation:
    a____#(__(X,Y),Z) = 8X + 4Y + 2Z + 4 >= 2Z + 1 = mark#(Z)
    
    a____#(__(X,Y),Z) = 8X + 4Y + 2Z + 4 >= 2Y + 1 = mark#(Y)
    
    a____#(__(X,Y),Z) = 8X + 4Y + 2Z + 4 >= 4Y + 2Z = a____#(mark(Y),mark(Z))
    
    a____#(__(X,Y),Z) = 8X + 4Y + 2Z + 4 >= 2X + 1 = mark#(X)
    
    a____#(__(X,Y),Z) = 8X + 4Y + 2Z + 4 >= 4X + 4Y + 2Z + 2 = a____#(mark(X),a____(mark(Y),mark(Z)))
    
    a____#(X,nil()) = 4X + 4 >= 2X + 1 = mark#(X)
    
    a____#(nil(),X) = 2X + 8 >= 2X + 1 = mark#(X)
    
    a__U11#(tt()) = 5 >= 4 = a__U12#(tt())
    
    a__isNePal#(__(I,__(P,I))) = 3I + 2P + 7 >= 5 = a__U11#(tt())
    
    mark#(__(X1,X2)) = 4X1 + 2X2 + 3 >= 2X2 + 1 = mark#(X2)
    
    mark#(__(X1,X2)) = 4X1 + 2X2 + 3 >= 2X1 + 1 = mark#(X1)
    
    mark#(__(X1,X2)) = 4X1 + 2X2 + 3 >= 4X1 + 2X2 = a____#(mark(X1),mark(X2))
    
    mark#(U11(X)) = 10X + 5 >= 2X + 1 = mark#(X)
    
    mark#(U11(X)) = 10X + 5 >= X + 4 = a__U11#(mark(X))
    
    mark#(U12(X)) = 4X + 5 >= 2X + 1 = mark#(X)
    
    mark#(U12(X)) = 4X + 5 >= X + 3 = a__U12#(mark(X))
    
    mark#(isNePal(X)) = 2X + 11 >= 2X + 1 = mark#(X)
    
    mark#(isNePal(X)) = 2X + 11 >= X + 5 = a__isNePal#(mark(X))
    
    a____(__(X,Y),Z) = 4X + 2Y + Z + 3 >= 2X + 2Y + Z + 2 = a____(mark(X),a____(mark(Y),mark(Z)))
    
    a____(X,nil()) = 2X + 3 >= X = mark(X)
    
    a____(nil(),X) = X + 5 >= X = mark(X)
    
    a__U11(tt()) = 7 >= 4 = a__U12(tt())
    
    a__U12(tt()) = 4 >= 1 = tt()
    
    a__isNePal(__(I,__(P,I))) = 3I + 2P + 7 >= 7 = a__U11(tt())
    
    mark(__(X1,X2)) = 2X1 + X2 + 1 >= 2X1 + X2 + 1 = a____(mark(X1),mark(X2))
    
    mark(U11(X)) = 5X + 2 >= 5X + 2 = a__U11(mark(X))
    
    mark(U12(X)) = 2X + 2 >= 2X + 2 = a__U12(mark(X))
    
    mark(isNePal(X)) = X + 5 >= X + 5 = a__isNePal(mark(X))
    
    mark(nil()) = 2 >= 2 = nil()
    
    mark(tt()) = 1 >= 1 = tt()
    
    a____(X1,X2) = 2X1 + X2 + 1 >= 2X1 + X2 + 1 = __(X1,X2)
    
    a__U11(X) = 5X + 2 >= 5X + 2 = U11(X)
    
    a__U12(X) = 2X + 2 >= 2X + 2 = U12(X)
    
    a__isNePal(X) = X + 5 >= X + 5 = isNePal(X)
   problem:
    DPs:
     
    TRS:
     a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
     a____(X,nil()) -> mark(X)
     a____(nil(),X) -> mark(X)
     a__U11(tt()) -> a__U12(tt())
     a__U12(tt()) -> tt()
     a__isNePal(__(I,__(P,I))) -> a__U11(tt())
     mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
     mark(U11(X)) -> a__U11(mark(X))
     mark(U12(X)) -> a__U12(mark(X))
     mark(isNePal(X)) -> a__isNePal(mark(X))
     mark(nil()) -> nil()
     mark(tt()) -> tt()
     a____(X1,X2) -> __(X1,X2)
     a__U11(X) -> U11(X)
     a__U12(X) -> U12(X)
     a__isNePal(X) -> isNePal(X)
   Qed