YES

   1: +(x1,0()) -> x1
   2: +(x1,s(x2)) -> s(+(x1,x2))
   3: +(0(),x2) -> x2
   4: +(s(x1),x2) -> s(+(x1,x2))
   5: dbl(x1) -> +(x1,x1)
   6: +(+(x1,x2),x3) -> +(x1,+(x2,x3))
   7: +(x1,x2) -> +(x2,x1)
   8: dbl(+(x1,x2)) -> +(dbl(x1),dbl(x2))

@Jouannaud and Kirchner's criterion
--- R
   1: +(x1,0()) -> x1
   2: +(x1,s(x2)) -> s(+(x1,x2))
   3: +(0(),x2) -> x2
   4: +(s(x1),x2) -> s(+(x1,x2))
   5: dbl(x1) -> +(x1,x1)
   6: +(+(x1,x2),x3) -> +(x1,+(x2,x3))
   7: +(x1,x2) -> +(x2,x1)
   8: dbl(+(x1,x2)) -> +(dbl(x1),dbl(x2))

--- S
   1: +(x1,0()) -> x1
   2: +(x1,s(x2)) -> s(+(x1,x2))
   3: +(0(),x2) -> x2
   4: +(s(x1),x2) -> s(+(x1,x2))
   5: dbl(x1) -> +(x1,x1)
   6: +(+(x1,x2),x3) -> +(x1,+(x2,x3))
   7: +(x1,x2) -> +(x2,x1)
   8: dbl(+(x1,x2)) -> +(dbl(x1),dbl(x2))