YES

1 decompositions
 #0 -----------
   1: +(x,0()) -> x
   2: +(x,s(y)) -> s(+(x,y))
   3: +(0(),y) -> y
   4: +(s(x),y) -> s(+(x,y))
   5: dbl(x) -> +(x,x)
   6: +(+(x,y),z) -> +(x,+(y,z))
   7: +(x,y) -> +(y,x)

@Jouannaud and Kirchner's criterion
--- R
   1: +(x,0()) -> x
   2: +(x,s(y)) -> s(+(x,y))
   3: +(0(),y) -> y
   4: +(s(x),y) -> s(+(x,y))
   5: dbl(x) -> +(x,x)
   6: +(+(x,y),z) -> +(x,+(y,z))
   7: +(x,y) -> +(y,x)

--- S
   1: +(x,0()) -> x
   2: +(x,s(y)) -> s(+(x,y))
   3: +(0(),y) -> y
   4: +(s(x),y) -> s(+(x,y))
   5: dbl(x) -> +(x,x)
   6: +(+(x,y),z) -> +(x,+(y,z))
   7: +(x,y) -> +(y,x)