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

precedence:

  s > f > g > 0