YES

TRS:

  g(f(x,y),z) -> f(x,g(y,z))
  g(h(x,y),z) -> g(x,f(y,z))
  g(x,h(y,z)) -> h(g(x,y),z)

max/plus interpretations on N:

  g_A(x1,x2) = max{6, -4, 1 + x2}
  g#_A(x1,x2) = max{17, 1, 4 + x2}
  f_A(x1,x2) = max{4, -5, -4 + x2}
  f#_A(x1,x2) = max{0, 0, 2 + x2}
  h_A(x1,x2) = max{11, 6 + x1, -5}
  h#_A(x1,x2) = max{0, 16, -2}

precedence:

  g > f = h