YES

TRS:

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

linear polynomial interpretations on N:

  f_A(x1,x2) = 0
  f#_A(x1,x2) = x1 + x2
  a_A = 2
  a#_A = 1
  g_A(x1) = 1
  g#_A(x1) = 1
  b_A = 1
  b#_A = 0

precedence:

  f > a = g > b