YES

TRS:

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

max/plus interpretations on N:

  f_A(x1) = max{4, -4}
  f#_A(x1) = max{6, -1}
  g_A(x1) = max{4, -3}
  g#_A(x1) = max{0, 1 + x1}

precedence:

  f > g