This is one of just a few plants that have totally defeated me. Luckily, I moved after a few yrs. I thought it was morning glory when a sprout first appeared and put up a trellis, watered it, kept waiting for flowers... The next year I noticed the blooms but I thought they were weird and damaged from bugs and started trying to remove it. By then it was coming up on the other side of the house, going under the driveway - from roots that were connected to the original plant. It may have eaten that house by now, it was circling around it faster than I could follow, preparing to do an alligator-style death roll or snake-style constriction.
One of the other plants was at the same house, goutweed (Aegopodium.) I wasn't able to try smothering, but there is no way to dig that up. No. Way. It just keeps growing anyway, as if you hadn't even touched the shovel.
Sorry, Sally, I rambled...