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:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [isNePal](x0) = x0 + 2,
   
   [U12](x0) = x0,
   
   [U11](x0) = x0 + 1,
   
   [a__isNePal](x0) = x0 + 2,
   
   [a__U12](x0) = x0,
   
   [a__U11](x0) = x0 + 1,
   
   [tt] = 1,
   
   [nil] = 0,
   
   [mark](x0) = x0,
   
   [a____](x0, x1) = 2x0 + x1,
   
   [__](x0, x1) = 2x0 + x1
  orientation:
   a____(__(X,Y),Z) = 4X + 2Y + Z >= 2X + 2Y + Z = a____(mark(X),a____(mark(Y),mark(Z)))
   
   a____(X,nil()) = 2X >= X = mark(X)
   
   a____(nil(),X) = X >= X = mark(X)
   
   a__U11(tt()) = 2 >= 1 = a__U12(tt())
   
   a__U12(tt()) = 1 >= 1 = tt()
   
   a__isNePal(__(I,__(P,I))) = 3I + 2P + 2 >= 2 = a__U11(tt())
   
   mark(__(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = a____(mark(X1),mark(X2))
   
   mark(U11(X)) = X + 1 >= X + 1 = a__U11(mark(X))
   
   mark(U12(X)) = X >= X = a__U12(mark(X))
   
   mark(isNePal(X)) = X + 2 >= X + 2 = a__isNePal(mark(X))
   
   mark(nil()) = 0 >= 0 = nil()
   
   mark(tt()) = 1 >= 1 = tt()
   
   a____(X1,X2) = 2X1 + X2 >= 2X1 + X2 = __(X1,X2)
   
   a__U11(X) = X + 1 >= X + 1 = U11(X)
   
   a__U12(X) = X >= X = U12(X)
   
   a__isNePal(X) = X + 2 >= X + 2 = isNePal(X)
  problem:
   a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
   a____(X,nil()) -> mark(X)
   a____(nil(),X) -> mark(X)
   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
   
   interpretation:
    [isNePal](x0) = 7x0,
    
    [U12](x0) = 2x0,
    
    [U11](x0) = x0,
    
    [a__isNePal](x0) = 7x0,
    
    [a__U12](x0) = 2x0,
    
    [a__U11](x0) = x0,
    
    [tt] = 0,
    
    [nil] = 1,
    
    [mark](x0) = x0,
    
    [a____](x0, x1) = x0 + x1,
    
    [__](x0, x1) = x0 + x1
   orientation:
    a____(__(X,Y),Z) = X + Y + Z >= X + Y + Z = a____(mark(X),a____(mark(Y),mark(Z)))
    
    a____(X,nil()) = X + 1 >= X = mark(X)
    
    a____(nil(),X) = X + 1 >= X = mark(X)
    
    a__U12(tt()) = 0 >= 0 = tt()
    
    a__isNePal(__(I,__(P,I))) = 14I + 7P >= 0 = a__U11(tt())
    
    mark(__(X1,X2)) = X1 + X2 >= X1 + X2 = a____(mark(X1),mark(X2))
    
    mark(U11(X)) = X >= X = a__U11(mark(X))
    
    mark(U12(X)) = 2X >= 2X = a__U12(mark(X))
    
    mark(isNePal(X)) = 7X >= 7X = a__isNePal(mark(X))
    
    mark(nil()) = 1 >= 1 = nil()
    
    mark(tt()) = 0 >= 0 = tt()
    
    a____(X1,X2) = X1 + X2 >= X1 + X2 = __(X1,X2)
    
    a__U11(X) = X >= X = U11(X)
    
    a__U12(X) = 2X >= 2X = U12(X)
    
    a__isNePal(X) = 7X >= 7X = isNePal(X)
   problem:
    a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
    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
    
    interpretation:
     [isNePal](x0) = 2x0,
     
     [U12](x0) = 2x0 + 1,
     
     [U11](x0) = x0 + 6,
     
     [a__isNePal](x0) = 2x0,
     
     [a__U12](x0) = 2x0 + 1,
     
     [a__U11](x0) = x0 + 6,
     
     [tt] = 2,
     
     [nil] = 0,
     
     [mark](x0) = x0,
     
     [a____](x0, x1) = x0 + x1 + 2,
     
     [__](x0, x1) = x0 + x1 + 2
    orientation:
     a____(__(X,Y),Z) = X + Y + Z + 4 >= X + Y + Z + 4 = a____(mark(X),a____(mark(Y),mark(Z)))
     
     a__U12(tt()) = 5 >= 2 = tt()
     
     a__isNePal(__(I,__(P,I))) = 4I + 2P + 8 >= 8 = a__U11(tt())
     
     mark(__(X1,X2)) = X1 + X2 + 2 >= X1 + X2 + 2 = a____(mark(X1),mark(X2))
     
     mark(U11(X)) = X + 6 >= X + 6 = a__U11(mark(X))
     
     mark(U12(X)) = 2X + 1 >= 2X + 1 = a__U12(mark(X))
     
     mark(isNePal(X)) = 2X >= 2X = a__isNePal(mark(X))
     
     mark(nil()) = 0 >= 0 = nil()
     
     mark(tt()) = 2 >= 2 = tt()
     
     a____(X1,X2) = X1 + X2 + 2 >= X1 + X2 + 2 = __(X1,X2)
     
     a__U11(X) = X + 6 >= X + 6 = U11(X)
     
     a__U12(X) = 2X + 1 >= 2X + 1 = U12(X)
     
     a__isNePal(X) = 2X >= 2X = isNePal(X)
    problem:
     a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
     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
     
     interpretation:
      [isNePal](x0) = 2x0 + 4,
      
      [U12](x0) = x0 + 3,
      
      [U11](x0) = 2x0,
      
      [a__isNePal](x0) = 2x0 + 4,
      
      [a__U12](x0) = x0 + 3,
      
      [a__U11](x0) = 2x0,
      
      [tt] = 0,
      
      [nil] = 0,
      
      [mark](x0) = x0,
      
      [a____](x0, x1) = 2x0 + x1,
      
      [__](x0, x1) = 2x0 + x1
     orientation:
      a____(__(X,Y),Z) = 4X + 2Y + Z >= 2X + 2Y + Z = a____(mark(X),a____(mark(Y),mark(Z)))
      
      a__isNePal(__(I,__(P,I))) = 6I + 4P + 4 >= 0 = a__U11(tt())
      
      mark(__(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = a____(mark(X1),mark(X2))
      
      mark(U11(X)) = 2X >= 2X = a__U11(mark(X))
      
      mark(U12(X)) = X + 3 >= X + 3 = a__U12(mark(X))
      
      mark(isNePal(X)) = 2X + 4 >= 2X + 4 = a__isNePal(mark(X))
      
      mark(nil()) = 0 >= 0 = nil()
      
      mark(tt()) = 0 >= 0 = tt()
      
      a____(X1,X2) = 2X1 + X2 >= 2X1 + X2 = __(X1,X2)
      
      a__U11(X) = 2X >= 2X = U11(X)
      
      a__U12(X) = X + 3 >= X + 3 = U12(X)
      
      a__isNePal(X) = 2X + 4 >= 2X + 4 = isNePal(X)
     problem:
      a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
      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)
     KBO Processor:
      weight function:
       w0 = 1
       w(isNePal) = w(U12) = w(U11) = w(a__isNePal) = w(a__U12) = w(a__U11) = w(
       tt) = w(nil) = 1
       w(mark) = w(a____) = w(__) = 0
      precedence:
       mark > a__isNePal ~ a__U12 ~ a__U11 ~ a____ > isNePal ~ U12 ~ U11 ~ tt ~ nil ~ __
      problem:
       
      Qed