YES

TRS:

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

linear polynomial interpretations on N:

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

precedence:

  f > g