YES

TRS:

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

linear polynomial interpretations on N:

  f_A(x1,x2) = x1 + x2
  f#_A(x1,x2) = x2
  a_A = 1
  a#_A = 0
  g_A(x1) = x1 + 1
  g#_A(x1) = 0

precedence:

  f > a = g