YES

TRS:

  sum(0()) -> 0()
  sum(s(x)) -> +(sum(x),s(x))
  +(x,0()) -> x
  +(x,s(y)) -> s(+(x,y))

linear polynomial interpretations on N:

  sum_A(x1) = x1 + 1
  sum#_A(x1) = x1 + 3
  0_A = 1
  0#_A = 0
  s_A(x1) = x1
  s#_A(x1) = 0
  +_A(x1,x2) = x1
  +#_A(x1,x2) = x1 + 1

precedence:

  sum > + > 0 = s