YES

TRS:

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

linear polynomial interpretations on N:

  double_A(x1) = x1 + 1
  double#_A(x1) = 2
  0_A = 1
  0#_A = 0
  s_A(x1) = 1
  s#_A(x1) = 0
  +_A(x1,x2) = x1 + 1
  +#_A(x1,x2) = 1

precedence:

  + > s > double > 0