What's funny is that math people know this is impossible and will never attempt it, but it's quite easy to write something practically useful that does the job

What's funny is that math people know this is impossible and will never attempt it, but it's quite easy to write something practically useful that does the job most of the way. It's possible for static analysis tools to identify many loops that will never end. E.g. in Java if there's no break or return and the guard is a boolean that is never written to and no runtime class loading is used. It can be very valuable to have static analysis tools in an organization, I know my own company has them, and we don't share them. IBM as well puts tons of work into it. Motorola has shared one of their tools. Every bug and issue your tool can find is one much more cheaply solved. Similarly, the client may be doing coding education, or interview, or other software where just a few limited lines and limited operations need to be checked, or it is OK to say if you hit n^4 loops you lose, etc..