YES

TRS:

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

max/plus interpretations on N:

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

precedence:

  h > g > f