YES

TRS:

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

max/plus interpretations on N:

  +_A(x1,x2) = max{2, x1, 14 + x2}
  +#_A(x1,x2) = max{1, 28, 15 + x2}
  0_A = 25
  0#_A = 23
  s_A(x1) = max{1, x1}
  s#_A(x1) = max{26, 2}
  f_A(x1) = max{22, 13 + x1}
  f#_A(x1) = max{22, 24}
  g_A(x1) = max{1, 8 + x1}
  g#_A(x1) = max{25, 6 + x1}
  h_A(x1,x2) = max{22, -3 + x1, 15 + x2}
  h#_A(x1,x2) = max{0, 27, 19 + x2}

precedence:

  g > h > + > s > f > 0