YES

TRS:

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

linear polynomial interpretations on N:

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

precedence:

  0 > g = f > s