YES

TRS:

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

linear polynomial interpretations on N:

  bin_A(x1,x2) = x1 + x2 + 1
  bin#_A(x1,x2) = 2
  0_A = 1
  0#_A = 0
  s_A(x1) = x1 + 1
  s#_A(x1) = 1
  +_A(x1,x2) = 0
  +#_A(x1,x2) = 0

precedence:

  bin = + > s > 0