Would this not be a good example of a closed loop paradox?

Say you had a time machine, and went back in time, killed whoever was your father, and had sex with your mother. Thus you would be making yourself, who eventually would go back in time to do the same. Is this not a perfect example of a closed loop paradox? Also consider if you went back in time after that, and killed yourself before you had sex with your mother. Wouldn’t all versions of you dissapear unless you had a paradox machine?