I think I know, but would love some input

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So, I just closed on a duplex with two tenants. I am going to renew the one, they have a month to month in place. The second is a problem tenant that I have decided to not give a chance. They have a 12 month in place, which expires in one month. The lease terms that I have inherited state the renewal is not automatic and must be done in writing. No other particulars are mentioned in the lease. I have not received any paperwork stating the lease has been renewed (though I suppose it could be out there). The thing is, WI law says a landlord must provide 60 days notice if a 12 month is going to be renewed or not - the lease says nothing about this either way. I am thinking I must give 60 days, but I would rather not!!! Any ideas? Or am I writing just to make myself feel better?

The tenant is horrible. They have numerous evictions, a theft record, the good tenant says they steal her stuff and their kids pull pieces of the house off (siding corners), and best for last, when they failed to pay the electric and it got turned off, they switched the meters, which of course is dangerous and put the good tenant in a mess with the electric co that was sending her the bills!!! LOL. Core BS and I don't play.  

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Are there any laws there on how much of an increase you can make in rent for the next lease period?   Instead of throwing them out, perhaps it would be easier to make them want to leave?  Just a thought...