YES

1 decompositions
 #1 -----------
   2: +(x1,0()) -> x1
   4: +(-(1()),1()) -> 0()
   5: -(0()) -> 0()
   6: -(-(x1)) -> x1
   7: -(+(x1,x2)) -> +(-(x1),-(x2))
   8: +(+(x1,x2),x3) -> +(x1,+(x2,x3))
   9: +(x1,x2) -> +(x2,x1)

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

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


NOTE: input TRS is reduced

original is
   1: +(0(),x1) -> x1
   2: +(x1,0()) -> x1
   3: +(1(),-(1())) -> 0()
   4: +(-(1()),1()) -> 0()
   5: -(0()) -> 0()
   6: -(-(x1)) -> x1
   7: -(+(x1,x2)) -> +(-(x1),-(x2))
   8: +(+(x1,x2),x3) -> +(x1,+(x2,x3))
   9: +(x1,x2) -> +(x2,x1)

reduced to
   2: +(x1,0()) -> x1
   4: +(-(1()),1()) -> 0()
   5: -(0()) -> 0()
   6: -(-(x1)) -> x1
   7: -(+(x1,x2)) -> +(-(x1),-(x2))
   8: +(+(x1,x2),x3) -> +(x1,+(x2,x3))
   9: +(x1,x2) -> +(x2,x1)