I would ask around to your neighbors and confirm if everything in the neighborhood was built with clay sewer/wastewater piping to the city sewer. If so, very good chance of pipe breakage. My sister-in-law had this problem. They found with a camera down the pipe. Also, ground settling at a foundation or otherwise can break old clay pipes.
Unless you have females flushing female things (i.e. tampons and pads) down your pipes or something big and absorbent, it might be hard to get that cling clogged up. The house I lived in at college had a sewer back up due to 4 females living in the house before us and flushing those things. I know because the plumber snaked them out through the cleanout.
Also, if you don't plan to be in the house forever, you can have the plumbers route something through broken clay pipes to clean as much tree root out as possible, but this is a "temporary" fix.