YES

TRS:

  norm(nil()) -> 0()
  norm(g(x,y)) -> s(norm(x))
  f(x,nil()) -> g(nil(),x)
  f(x,g(y,z)) -> g(f(x,y),z)
  rem(nil(),y) -> nil()
  rem(g(x,y),0()) -> g(x,y)
  rem(g(x,y),s(z)) -> rem(x,z)

max/plus interpretations on N:

  norm_A(x1) = max{9, -1}
  norm#_A(x1) = max{8, 4 + x1}
  nil_A = 2
  nil#_A = 8
  0_A = 1
  0#_A = 7
  g_A(x1,x2) = max{7, x1, 5}
  g#_A(x1,x2) = max{1, 3, 3}
  s_A(x1) = max{1, 1}
  s#_A(x1) = max{0, 1 + x1}
  f_A(x1,x2) = max{7, -1, 1}
  f#_A(x1,x2) = max{3, 3, 3}
  rem_A(x1,x2) = max{0, x1, -1}
  rem#_A(x1,x2) = max{0, 2, 3}

precedence:

  nil > norm = f > 0 = g > s = rem