If that is the case, the Copper Sulfate solution is a good one. They sell it in the plumbing department of the hardware store. It's not expensive, but you have to keep on top of it and do it regularly.
I had this happen, and the roots got too thick so I had to have it dug up and fixed. The city's responsibility ends at their pipe, which makes the junction your problem. Sorry.
Go to the end of your property, dig up the end of your pipe and stick a new piece on it and shoot it into the street! k probably not a good idea but it would be fun!!!