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)))

max/plus interpretations on N:

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

precedence:

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