Can you name this groundcover?

This groundcover seems to grow wild in Tennessee. Not sure if native or introduced.

It has leaves about 1 inch long, 1/2 inch wide, very dark green, somewhat shiny, elliptic, yellowish veining, and I believe, the leaves are alternating. The margins are somewhat serrated. The stem is straight and semi-woody. It creeps across the ground, lower than mowing-level.

I have no idea about the roots.