I cut down some trees when I moved in 10 years ago. By this spring, most of them had rotted enough I could either break them up with an old axe, or cut a few roots and pull them out easily. Two were a bit of a pain. One had many, many horizontal roots that I cut with a Sawzall and a pruning blade, the other ended up staying in the ground cut just-below ground level with the chainsaw.
I tried drilling holes and pouring the quick rot stuff in two of them years ago, and they were two of the more difficult ones to get rid of this year. Not worth the money or time for that stuff.