Aandew,
I have this same issue with my neighbor as well. Except my relationship with them is the nightmare from hell version. The question is have they or you done a legal survey on this issue? Just because the photo shows this or that doesn't mean it's the true property line unless a legal survey has been done.
Wisconsin Law for Adverse Possession:
Quoting Wis Stat § 893.25 - Adverse possession, not founded on written instrument.
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(1) An action for the recovery or the possession of real estate and a defense or counterclaim based on title to real estate are barred by uninterrupted adverse possession of 20 years, except as provided by s. 893.14 and 893.29. A person who, in connection with his or her predecessors in interest, is in uninterrupted adverse possession of real estate for 20 years, except as provided by s. 893.29, may commence an action to establish title under ch. 841.
(2) Real estate is possessed adversely under this section:
(a) Only if the person possessing it, in connection with his or her predecessors in interest, is in actual continued occupation under claim of title, exclusive of any other right; and
(b) Only to the extent that it is actually occupied and:
1. Protected by a substantial enclosure; or
2. Usually cultivated or improved.
and look at this site about Easements:
http://www.wrpla.org/Resources/IntroductionEasements.htm
Now, here is my take on this issue.... don't let it lay with a good neighbor, because if the neighbor moves then your faced with a possible HUGE problem. If you get the nightmare from hell neigbhors that move in.
You can do what I attempted. Offer to buy that section of ground from them. Take in mind you will have survey costs, title costs etc.. etc.. with this. So keep the costs in mind when figuring the offer. Since you know the sq ft. of the area I would say figure the cost you paid for the lot. break it down by sq ft then figure that $ into that area.
You don't have adverse possesion, you could shoot for a easement but that in it's self is a tough one. If you have been using this land and the other owner hasn't then Lets hope they will just sell it to you.
with all that being said. "It's always nice to have a lawyer look over everything once you find out what your nieghbor wants to do"
Good luck