Is Oil of Oregano Safe with Coumadin?

I am on coumadin, which reacts with many herbals used for combating colds and flu. Is oil of oregano safe with coumadin (warfarin)?

Oil of oregano may discourage blood clotting and therefore be unsafe for use with coumadin.
Aristolochic acid I and II are found in the oregano plant. Aristolochic acid I and II inhibit thrombin activity. Thrombin promotes blood clots by affecting the conversion of fibrinogen to fibrin, which promotes blood clotting.