YES

TRS:

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

linear polynomial interpretations on N:

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

precedence:

  + > 0 = s