YES

TRS:

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

max/plus interpretations on N:

  g_A(x1) = max{5, -3}
  g#_A(x1) = max{0, 8 + x1}
  h_A(x1) = max{3, 4}
  h#_A(x1) = max{1, 2 + x1}
  f_A(x1,x2) = max{0, -2, 0}
  f#_A(x1,x2) = max{3, x1, 4}

precedence:

  g = f > h