IANAL.
And I would say it would depend. I tend to doubt it, especially if the actual owner were occupying the property and keeping it maintained but for that strip. It could be argued that the adverse possessor mowed before the actual owner had a chance to. But in any case, if the actual owner is concerned, a polite conversation to the neighbor is in order. If nothing else, it breaks the continuity of the possessory timeframe and restarts the clock. (But to prove that, a way to document the conversation would be a good thing.)
Can I just shoot hm in the face? I'd really like to just shoot him in the face. He's a complete male sexual organ. His heirs can even have that little strip of dirt.