YES

TRS:

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

linear polynomial interpretations on N:

  g_A(x1,x2) = x1
  g#_A(x1,x2) = x1
  f_A(x1) = x1 + 1
  f#_A(x1) = 0
  h_A(x1,x2) = x1
  h#_A(x1,x2) = x1 + 1

precedence:

  g > h > f