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)))

linear polynomial interpretations on N:

  f_A(x1) = x1
  f#_A(x1) = x1 + 3
  0_A = 1
  0#_A = 6
  1_A = 0
  1#_A = 5
  s_A(x1) = x1
  s#_A(x1) = 0
  g_A(x1,x2) = x2
  g#_A(x1,x2) = x2 + 2
  +_A(x1,x2) = x1
  +#_A(x1,x2) = x1 + 1

precedence:

  0 = + > 1 = s > f > g