YES

TRS:

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

max/plus interpretations on N:

  f_A(x1) = max{1, -5}
  f#_A(x1) = max{3, 11 + x1}
  g_A(x1) = max{7, 2 + x1}
  g#_A(x1) = max{1, 2}
  a_A(x1,x2) = max{3, -6 + x1, 0}
  a#_A(x1,x2) = max{0, 0, 0}

precedence:

  f > g > a