YES

   1: +(x1,0()) -> x1
   2: +(x1,s(x2)) -> s(+(x1,x2))
   3: d(0()) -> 0()
   4: d(s(x1)) -> s(s(d(x1)))
   5: f(0()) -> 0()
   6: f(s(x1)) -> +(+(s(x1),s(x1)),s(x1))
   7: f(g(0())) -> +(+(g(0()),g(0())),g(0()))
   8: g(x1) -> s(d(x1))

@Rule Labeling
--- R
   1: +(x1,0()) -> x1
   2: +(x1,s(x2)) -> s(+(x1,x2))
   3: d(0()) -> 0()
   4: d(s(x1)) -> s(s(d(x1)))
   5: f(0()) -> 0()
   6: f(s(x1)) -> +(+(s(x1),s(x1)),s(x1))
   7: f(g(0())) -> +(+(g(0()),g(0())),g(0()))
   8: g(x1) -> s(d(x1))

--- S
   1: +(x1,0()) -> x1
   2: +(x1,s(x2)) -> s(+(x1,x2))
   3: d(0()) -> 0()
   4: d(s(x1)) -> s(s(d(x1)))
   5: f(0()) -> 0()
   6: f(s(x1)) -> +(+(s(x1),s(x1)),s(x1))
   7: f(g(0())) -> +(+(g(0()),g(0())),g(0()))
   8: g(x1) -> s(d(x1))