I'm not sure this follows. It doesn't halt because the "program" reaches an end, it's halts because the hardware fails. If you are running a category B program with an anvil attached to a timer over the computer, it doesn't become a category A program. It's just a category B program that wasn't allowed to continue.

-edit- Also, this logic would lead us to believe that category B and C programs can't exist in our universe since, according to our best current understanding, the universe will end eventually, presumably ending any program running within the universe as well, therefore we can "prove" that every program is a category A program that will come to a halt.