YES

TRS:

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

linear polynomial interpretations on N:

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

precedence:

  f > g