YES

TRS:

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

max/plus interpretations on N:

  g_A(x1,x2,x3) = max{4, 5, 5 + x2, x3}
  g#_A(x1,x2,x3) = max{2, 1, -1 + x2, 3}
  a_A = 6
  a#_A = 4
  b_A = 1
  b#_A = 0

precedence:

  g > a > b