[turingfeel]

> The algorithm can run infinitely.

Really? Isn't the whole point of proving the conjecture attempting to answer that question? If you have an example of a starting integer that causes the algorithm to run infintely I'd be eager to hear it.

[owenpalmer]

Ending up with an infinite repeating sequence and "running infinitely" are not the same thing

[eru]

Just use a slightly different rule that stops when it reaches 1.

[hansvm]

Has the acyclic unbounded case been ruled out?

[renewiltord]

Man, I think if you think this level of precision is hard to disambiguate I wonder how you handle the notational abuse common in Mathematics.

It might not be the field for you.