YES

TRS:

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

max/plus interpretations on N:

  f_A(x1) = max{11, -10}
  f#_A(x1) = max{0, 27}
  g_A(x1,x2) = max{10, 5 + x1, -11}
  g#_A(x1,x2) = max{29, 13 + x1, 18 + x2}
  a_A = 11
  a#_A = 26
  h_A(x1,x2) = max{7, -20, -12}
  h#_A(x1,x2) = max{28, -1, 12 + x2}

precedence:

  g > h > f > a