YES

TRS:

  f(x,0()) -> s(0())
  f(s(x),s(y)) -> s(f(x,y))
  g(0(),x) -> g(f(x,x),x)

max/plus interpretations on N:

  f_A(x1,x2) = max{1, -2, -2}
  f#_A(x1,x2) = max{1, -4, -5}
  0_A = 5
  0#_A = 0
  s_A(x1) = max{1, 1}
  s#_A(x1) = max{1, -4 + x1}
  g_A(x1,x2) = max{0, x1, 0}
  g#_A(x1,x2) = max{2, -2 + x1, 0}

precedence:

  g > f > 0 = s