YES

TRS:

  f(g(x)) -> f(a(g(g(f(x))),g(f(x))))

linear polynomial interpretations on N:

  f_A(x1) = 1
  f#_A(x1) = x1 + 1
  g_A(x1) = x1 + 1
  g#_A(x1) = 0
  a_A(x1,x2) = 0
  a#_A(x1,x2) = 0

precedence:

  g > f > a