It doesn't. Flip things around and you get something tractable, though incomplete. Unsolvable problem: reject any loop that is provably infinite. Solvable pro

It doesn't. Flip things around and you get something tractable, though incomplete. Unsolvable problem: reject any loop that is provably infinite. Solvable problem: reject any loop that isn't provably finite. The trade off is that there will always be some loops that in fact always do terminate, but that the verifier can't prove do.