YES

TRS:

  f(0()) -> 1()
  f(s(x)) -> g(x,s(x))
  g(0(),y) -> y
  g(s(x),y) -> g(x,+(y,s(x)))
  +(x,0()) -> x
  +(x,s(y)) -> s(+(x,y))
  g(s(x),y) -> g(x,s(+(y,x)))

max/plus interpretations on N:

  f_A(x1) = max{4, 4 + x1}
  f#_A(x1) = max{4, 4 + x1}
  0_A = 0
  0#_A = 0
  1_A = 1
  1#_A = 1
  s_A(x1) = max{3, x1}
  s#_A(x1) = max{3, x1}
  g_A(x1,x2) = max{2, 2 + x1, 2 + x2}
  g#_A(x1,x2) = max{2, 2 + x1, 2 + x2}
  +_A(x1,x2) = max{1, x1, x2}
  +#_A(x1,x2) = max{1, x1, x2}

precedence:

  g > 0 = + > 1 = s > f