YES

TRS:

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

max/plus interpretations on N:

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

precedence:

  f > h