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

precedence:

  f = g > b > a