YES

TRS:

  f(f(X)) -> f(g(f(g(f(X)))))
  f(g(f(X))) -> f(g(X))

linear polynomial interpretations on N:

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

precedence:

  f > g