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))
  D(minus(x)) -> minus(D(x))
  D(div(x,y)) -> -(div(D(x),y),div(*(x,D(y)),pow(y,2())))
  D(ln(x)) -> div(D(x),x)
  D(pow(x,y)) -> +(*(*(y,pow(x,-(y,1()))),D(x)),*(*(pow(x,y),ln(x)),D(y)))

linear polynomial interpretations on N:

  D_A(x1) = 1
  D#_A(x1) = 4
  t_A = 1
  t#_A = 0
  1_A = 1
  1#_A = 1
  constant_A = 1
  constant#_A = 1
  0_A = 0
  0#_A = 0
  +_A(x1,x2) = x2
  +#_A(x1,x2) = x1 + 2
  *_A(x1,x2) = 1
  *#_A(x1,x2) = 3
  -_A(x1,x2) = 1
  -#_A(x1,x2) = 1
  minus_A(x1) = 1
  minus#_A(x1) = 0
  div_A(x1,x2) = 1
  div#_A(x1,x2) = 1
  pow_A(x1,x2) = x1 + 1
  pow#_A(x1,x2) = 2
  2_A = 1
  2#_A = 0
  ln_A(x1) = 1
  ln#_A(x1) = 0

precedence:

  D = constant > 0 = + = minus = div > pow = 2 > 1 = * = - = ln > t