YES

TRS:

  D(t()) -> 1()
  D(constant()) -> 0()
  D(+(x,y)) -> +(D(x),D(y))
  D(*(x,y)) -> +(*(y,D(x)),*(x,D(y)))
  D(-(x,y)) -> -(D(x),D(y))

linear polynomial interpretations on N:

  D_A(x1) = 1
  D#_A(x1) = 1
  t_A = 1
  t#_A = 1
  1_A = 0
  1#_A = 0
  constant_A = 1
  constant#_A = 1
  0_A = 0
  0#_A = 0
  +_A(x1,x2) = 1
  +#_A(x1,x2) = 0
  *_A(x1,x2) = x1 + 1
  *#_A(x1,x2) = 0
  -_A(x1,x2) = 1
  -#_A(x1,x2) = 1

precedence:

  t > 1 > D = constant = - > 0 = + = *