As for my discrete math exam preparation our lecturer gave us a list of statements which we have to know how to proof in case if we have it in our test list. But I have some problems with this one The euclidean algorithm terminates for each input.
I understand the idea of the algorithm and the way it works but it is hard for me to come up with the idea how to prove it. I've been trying to find some information online but unfortunately there is almost nothing similar with the statement I have. Please can someone explain me what can be used as a proof.