MFP, yeah, the laws on adverse possession seem very strange in modern society. They were developed eons ago when there was lots of open land everywhere. The theory was that all land should be put to productive use, so if someone wasn't paying enough attention to his or her land to notice that there was a squatter on it, they probably weren't making full use of it. So if someone came upon some open land, the most productive thing for the law to sanction would be to let them use it (farm it, graze cattle on it, whatever), and if no one noticed for some set period of time, then the squatter should just get to own it. No reason to let open land just sit there if someone else wanted to put it to use.

Also, thank you MFP for reminding me that I had been intending to come back and supplement what I had written with a small bit of advice for EVA. If you're concerned that they may have actually built on your property, you should have a survey done. Once you know where the property line is and whether their house is over the line, the safest thing to do is to write them a very simple letter that says, "We have had a survey conducted and are aware that your home is built partially on our property. You have my permission to allow the structure to remain over the property line at this time. However, this grant of permission is subject to revocation at any time and without notice."

That way, you have documentation that their use is permissive (just like you have right now with the easement for their lawn), so there is no adverse possession issue.