It seems like this problem is unsolvable thanks to its ambiguity and generalization. It seems that if you are dealing with purely numeric input and the program halts whenever an end inequality is met then it would be, if not easy, at least possible to solve whether the program will halt in a finite amount of time. Since the input and halting conditions are abstractions and have no limitations towards their execution/implementation, testing whether or not the program will halt is certainly not possible in guaranteed finite amount of time.
--Jniederh 16:56, 16 November 2008 (UTC)
