YES

TRS:

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

max/plus interpretations on N:

  f_A(x1) = max{1, 1}
  f#_A(x1) = max{0, 1}
  s_A(x1) = max{6, 3 + x1}
  s#_A(x1) = max{2, 7}
  g_A(x1) = max{0, 1}
  g#_A(x1) = max{3, x1}
  0_A = 1
  0#_A = 5

precedence:

  s > g > f = 0