Invasive (?) Vine on my Texas Liveoak

I've looked at all the plants listed in the Invasive plant list at http://www.nps.gov/plants/alien/factmain.htm#pllists and still cannot identify what seems to be an invasive vine growing on my Texas Liveoak. Unfortunately, I do not have a picture at this time. It has smooth, round green leaves. So, far I have not seen any flowering, though I just bought this house and have not been around for a full season. It looks like the vine has been there for over twenty years. The vine at the base of the tree is over 6 inches in diameter. The roots run all through the flowerbed for many feet. They fork into other roots often.

I will try to get you a picture the next time I go over to the house (I'm remodeling and have not moved in yet), but does anyone know of any common vines that grow on Texas Liveoaks? It runs all the way up the trunk and has vines and leaves in the branches even at the very top of the tree. Any suggestions would be greatly appreciated. :)

Could it be Oriental Bittersweet?