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

MIT 6.00 Intro Computer Science (OCW)
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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.
Given that you are given the data you should be able to "dry run" the program. Infinite loops are not desireable.
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.

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