YES

TRS:

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

linear polynomial interpretations on N:

  g_A(x1) = x1
  g#_A(x1) = x1
  b_A = 3
  b#_A = 1
  f_A(x1) = 1
  f#_A(x1) = 2
  a_A = 1
  a#_A = 0

precedence:

  g > b = f > a