YES

TRS:

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

linear polynomial interpretations on N:

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

precedence:

  s > g > f = 0