YES

1 decompositions
 #0 -----------
   1: +(x,0()) -> x
   2: +(x,s(y)) -> s(+(x,y))
   3: +(x,p(y)) -> p(+(x,y))
   4: +(0(),y) -> y
   5: +(s(x),y) -> s(+(x,y))
   6: +(p(x),y) -> p(+(x,y))
   7: s(p(x)) -> x
   8: p(s(x)) -> x
   9: -(0()) -> 0()
  10: -(s(x)) -> p(-(x))
  11: -(p(x)) -> s(-(x))
  12: +(+(x,y),z) -> +(x,+(y,z))
  13: +(x,+(y,z)) -> +(+(x,y),z)
  14: -(+(x,y)) -> +(-(x),-(y))

@Jouannaud and Kirchner's criterion
--- R
   1: +(x,0()) -> x
   2: +(x,s(y)) -> s(+(x,y))
   3: +(x,p(y)) -> p(+(x,y))
   4: +(0(),y) -> y
   5: +(s(x),y) -> s(+(x,y))
   6: +(p(x),y) -> p(+(x,y))
   7: s(p(x)) -> x
   8: p(s(x)) -> x
   9: -(0()) -> 0()
  10: -(s(x)) -> p(-(x))
  11: -(p(x)) -> s(-(x))
  12: +(+(x,y),z) -> +(x,+(y,z))
  13: +(x,+(y,z)) -> +(+(x,y),z)
  14: -(+(x,y)) -> +(-(x),-(y))

--- S
   1: +(x,0()) -> x
   2: +(x,s(y)) -> s(+(x,y))
   3: +(x,p(y)) -> p(+(x,y))
   4: +(0(),y) -> y
   5: +(s(x),y) -> s(+(x,y))
   6: +(p(x),y) -> p(+(x,y))
   7: s(p(x)) -> x
   8: p(s(x)) -> x
   9: -(0()) -> 0()
  10: -(s(x)) -> p(-(x))
  11: -(p(x)) -> s(-(x))
  12: +(+(x,y),z) -> +(x,+(y,z))
  13: +(x,+(y,z)) -> +(+(x,y),z)
  14: -(+(x,y)) -> +(-(x),-(y))