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))

max/plus interpretations on N:

  D_A(x1) = max{1, 2 + x1}
  D#_A(x1) = max{5, 1 + x1}
  t_A = 1
  t#_A = 1
  1_A = 2
  1#_A = 0
  constant_A = 1
  constant#_A = 7
  0_A = 1
  0#_A = 6
  +_A(x1,x2) = max{3, x1, x2}
  +#_A(x1,x2) = max{5, 5, -2 + x2}
  *_A(x1,x2) = max{4, x1, x2}
  *#_A(x1,x2) = max{1, -3, 1}
  -_A(x1,x2) = max{5, 9 + x1, 7 + x2}
  -#_A(x1,x2) = max{0, 0, 0}

precedence:

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