YES

TRS:

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

linear polynomial interpretations on N:

  g_A(x1) = x1 + 3
  g#_A(x1) = x1 + 3
  0_A = 1
  0#_A = 1
  s_A(x1) = x1 + 2
  s#_A(x1) = x1 + 2
  f_A(x1) = x1 + 1
  f#_A(x1) = x1 + 1

precedence:

  0 > f > g > s