Question

I am supposed to decide whether an arbitrary computer program finishes running or runs forever

Answer 1

You can either do an algorithm analysis to check whether or not you are running into a infinite loop or you could try it out empirically. So yeah, in general, it's your call to decide whether or not the program is running forever.

Answer 2

Given that you are given the data you should be able to "dry run" the program. Infinite loops are not desireable.

Answer 3

bmp is right, but to know for certain you need to do the algorithm analysis - check all of your for and while loops etc. and make sure each test terminates.