YES

TRS:

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

linear polynomial interpretations on N:

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

precedence:

  f > g = h