YES

TRS:

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

max/plus interpretations on N:

  g_A(x1) = max{3, 1 + x1}
  g#_A(x1) = max{0, 5}
  s_A(x1) = max{1, -4 + x1}
  s#_A(x1) = max{4, 3}
  f_A(x1) = max{3, -3 + x1}
  f#_A(x1) = max{5, 2}
  0_A = 8
  0#_A = 1

precedence:

  g = f > s = 0