Before you file the adverse possession claim I strongly urge you to seek advice from a real estate lawyer familiar with adverse possession claims. If you file too early and put the true owner on notice that you intend to seek title by adverse possession the true owner may start the process to eject you and thus kill your adverse possession claim. When title to the property is obtained by the county in a tax foreclosure sale the SOL period may start when the city has actually provided the deed to the buyer. A federal appeals court decision suggests that is the case, but the state courts have not made a clear decision on that and ultimately the Supreme Court of Michigan has the final say on the issue. It might be prudent to wait until it has been 10 years from the date the city gave the deed to the buyer to avoid a problem of filing too early and alerting the true owner that he needs to take action. You want to be sure that you have all your ducks properly lined up here. The fee you pay the lawyer for a review and advice on this is a relatively small investment to get the property. If you don't do that and screw it up, you could lose your shot to get the property.

That you didn't pay property taxes does not appear to matter in Michigan like it does in some other states. And the deed from A to B would not restart the SOL for your adverse possession claim.