YES

TRS:

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

max/plus interpretations on N:

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

precedence:

  a > b > f > g = d