YES

TRS:

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

max/plus interpretations on N:

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

precedence:

  f > a = g > b