> there are a huge number of useful loops that do useful work and for which you can prove properties like termination
Exactly! If the loop doesn't terminate, then you obviously cannot show it. But if it does, then you should be able to (even if that requires some changes to help the tool)
> If the loop doesn't terminate, then you obviously cannot show it.
I don't think this is true for all loops either - some can be proven to never terminate, just like some can be proven to terminate. And some can't be proven either way.
Exactly! If the loop doesn't terminate, then you obviously cannot show it. But if it does, then you should be able to (even if that requires some changes to help the tool)