YES

1 decompositions
 #1 -----------
   1: -(0(),0()) -> 0()
   2: -(s(x1),0()) -> s(x1)
   3: -(x2,s(x3)) -> -(d(x2),x3)
   4: d(s(x4)) -> x4
   6: -(d(x7),x8) -> -(x7,s(x8))

@Rule Labeling
--- R
   1: -(0(),0()) -> 0()
   2: -(s(x1),0()) -> s(x1)
   3: -(x2,s(x3)) -> -(d(x2),x3)
   4: d(s(x4)) -> x4
   6: -(d(x7),x8) -> -(x7,s(x8))

--- S
   1: -(0(),0()) -> 0()
   2: -(s(x1),0()) -> s(x1)
   3: -(x2,s(x3)) -> -(d(x2),x3)
   4: d(s(x4)) -> x4
   6: -(d(x7),x8) -> -(x7,s(x8))


NOTE: input TRS is reduced

original is
   1: -(0(),0()) -> 0()
   2: -(s(x1),0()) -> s(x1)
   3: -(x2,s(x3)) -> -(d(x2),x3)
   4: d(s(x4)) -> x4
   5: -(s(x5),s(x6)) -> -(x5,x6)
   6: -(d(x7),x8) -> -(x7,s(x8))

reduced to
   1: -(0(),0()) -> 0()
   2: -(s(x1),0()) -> s(x1)
   3: -(x2,s(x3)) -> -(d(x2),x3)
   4: d(s(x4)) -> x4
   6: -(d(x7),x8) -> -(x7,s(x8))