YES

TRS:

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

linear polynomial interpretations on N:

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

precedence:

  0 > g > f