YES

TRS:

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

linear polynomial interpretations on N:

  f_A(x1,x2) = x1 + x2
  f#_A(x1,x2) = x1 + x2
  g_A(x1,x2) = x1 + x2
  g#_A(x1,x2) = x1 + x2
  h_A(x1) = x1 + 1
  h#_A(x1) = x1 + 1

precedence:

  f > g > h