YES

TRS:

  f(f(x)) -> f(x)
  g(0()) -> g(f(0()))

max/plus interpretations on N:

  f_A(x1) = max{1, -1}
  f#_A(x1) = max{0, 2}
  g_A(x1) = max{0, 1}
  g#_A(x1) = max{3, 1 + x1}
  0_A = 4
  0#_A = 4

precedence:

  f > g > 0