YES

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

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

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