YES

TRS:

  f(f(X)) -> f(a(b(f(X))))
  f(a(g(X))) -> b(X)
  b(X) -> a(X)

linear polynomial interpretations on N:

  f_A(x1) = 2
  f#_A(x1) = x1 + 1
  a_A(x1) = 1
  a#_A(x1) = 0
  b_A(x1) = 1
  b#_A(x1) = 1
  g_A(x1) = x1 + 1
  g#_A(x1) = 2

precedence:

  f = g > b > a