YES

TRS:

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

max/plus interpretations on N:

  f_A(x1,x2) = max{0, 2, -1}
  f#_A(x1,x2) = max{4, 1 + x1, 2}
  a_A = 4
  a#_A = 7
  g_A(x1,x2) = max{2, 1, -1}
  g#_A(x1,x2) = max{0, 5, 3}
  b_A = 0
  b#_A = 6

precedence:

  a > f > g > b