YES

TRS:

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

linear polynomial interpretations on N:

  f_A(x1,x2) = x2
  f#_A(x1,x2) = x1
  a_A = 3
  a#_A = 1
  g_A(x1,x2) = x2
  g#_A(x1,x2) = 2
  b_A = 1
  b#_A = 0

precedence:

  a > b > g > f