YES

TRS:

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

linear polynomial interpretations on N:

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

precedence:

  b > g > a > f