Each state law is different.  Illinois adverse possession law is not simple. For a more understandable (I've tried reading the statutes. Believe me it can be very confusing) summary see https://www.nolo.com/legal-encyclopedia/who-can-claim-property-based-adverse-possession-illinois.html 

 In Burdick's situation it's going to depend on the use and how long this has been going on.  If he and the neighbor can't come to an agreement the only solution is going to be a long and costly court battle.