It also may not be applicable if you don't actually have access to all memory states involved. E.g. when communicating with a 3rd party computer over a network.
It still is applicable, as long as you have a bound on the number of unknown states, however the number of computation steps in this case is so high that it is even less practical than the totally unpractical algorithm I proposed in my first comment.
Let's consider both computers (yours and 3rd party) as a single computational device, with a state represented by a pair of symbols, where the first represents your computer and the second the 3rd party's. Suppose your computer has N states and the other M. It's enough to run N * M + 1 computation steps -- if your program hasn't ended so far, it will never, for there's a certain state (a, b) that must have occured twice, by the pigeonhole principle.
Please keep in mind that this is all purely theoretical, and not at all practical. It's just a counterargument to other purely theoretical argument from unsolvability of halting problem.
