YES

1 decompositions
 #1 -----------
   4: +(0(),x2) -> x2
   5: +(s(x1),x2) -> s(+(x1,x2))
   6: +(p(x1),x2) -> p(+(x1,x2))
   7: s(p(x1)) -> x1
   8: p(s(x1)) -> x1
   9: -(0()) -> 0()
  10: -(s(x1)) -> p(-(x1))
  11: -(p(x1)) -> s(-(x1))
  12: +(+(x1,x2),x3) -> +(x1,+(x2,x3))
  13: +(x1,x2) -> +(x2,x1)
  14: -(+(x1,x2)) -> +(-(x1),-(x2))

@Jouannaud and Kirchner's criterion
--- R
   4: +(0(),x2) -> x2
   5: +(s(x1),x2) -> s(+(x1,x2))
   6: +(p(x1),x2) -> p(+(x1,x2))
   7: s(p(x1)) -> x1
   8: p(s(x1)) -> x1
   9: -(0()) -> 0()
  10: -(s(x1)) -> p(-(x1))
  11: -(p(x1)) -> s(-(x1))
  12: +(+(x1,x2),x3) -> +(x1,+(x2,x3))
  13: +(x1,x2) -> +(x2,x1)
  14: -(+(x1,x2)) -> +(-(x1),-(x2))

--- S
   4: +(0(),x2) -> x2
   5: +(s(x1),x2) -> s(+(x1,x2))
   6: +(p(x1),x2) -> p(+(x1,x2))
   7: s(p(x1)) -> x1
   8: p(s(x1)) -> x1
   9: -(0()) -> 0()
  10: -(s(x1)) -> p(-(x1))
  11: -(p(x1)) -> s(-(x1))
  12: +(+(x1,x2),x3) -> +(x1,+(x2,x3))
  13: +(x1,x2) -> +(x2,x1)
  14: -(+(x1,x2)) -> +(-(x1),-(x2))


NOTE: input TRS is reduced

original is
   1: +(x1,0()) -> x1
   2: +(x1,s(x2)) -> s(+(x1,x2))
   3: +(x1,p(x2)) -> p(+(x1,x2))
   4: +(0(),x2) -> x2
   5: +(s(x1),x2) -> s(+(x1,x2))
   6: +(p(x1),x2) -> p(+(x1,x2))
   7: s(p(x1)) -> x1
   8: p(s(x1)) -> x1
   9: -(0()) -> 0()
  10: -(s(x1)) -> p(-(x1))
  11: -(p(x1)) -> s(-(x1))
  12: +(+(x1,x2),x3) -> +(x1,+(x2,x3))
  13: +(x1,x2) -> +(x2,x1)
  14: -(+(x1,x2)) -> +(-(x1),-(x2))

reduced to
   4: +(0(),x2) -> x2
   5: +(s(x1),x2) -> s(+(x1,x2))
   6: +(p(x1),x2) -> p(+(x1,x2))
   7: s(p(x1)) -> x1
   8: p(s(x1)) -> x1
   9: -(0()) -> 0()
  10: -(s(x1)) -> p(-(x1))
  11: -(p(x1)) -> s(-(x1))
  12: +(+(x1,x2),x3) -> +(x1,+(x2,x3))
  13: +(x1,x2) -> +(x2,x1)
  14: -(+(x1,x2)) -> +(-(x1),-(x2))