Does your body usually eliminate the hpv viruses 6 and 11 that cause genital warts within 2 years? even if you have warts?

Define "eliminate": Anyone with a normal immune system will usually see the primary HPV infection with any strain become inactive within 2 years. Most people with warts would have the visible lesions lasered/frozen or chemically removed. However, HPV is a family of viruses well known for going into a hibernation phase after the initial infection. It can re-emerge in the future. They may not, but can.