Will over seeding with Bermuda get rid of St Augustine grass?

My neighbor has their St Augustine grass creeping over into my yard..We do not like St Augustine grass at all..The long vines of growth are easy to trip over...Our yard is Bermuda grass..If I mow the St Augustine grass real short in that spot in my yard and over seed it with Bermuda grass..will it crowd out the St. Augustine...I have tripped over that St. Augustine way too many times to count....