[E6300]

It's not a given that the input is infinite. If the used types in "Rob" then goes away forever, the program will neither terminate nor process an infinite number of non-"Ralph" strings. It will sit just sit there waiting (possibly in a loop, possibly not) for a hardware interrupt that will never arrive.

[colanderman]

For decidability to apply, the input needs to be known a priori in its entirety. Decidability is a mathematical statement about natural numbers (or any other countably infinite set); it has absolutely nothing to do with "paused" input or any notion of "interactivity".

The type of behavior you're concerned with does on the other hand fall squarely in the realm of temporal logics (e.g. TLA+), which do concern themselves with interactivity and indeterminate pauses. For example, the statement "so long as the user eventually inputs the string 'Ralph', the algorithm eventually terminates" is decidable for any finite state machine.

In other words, if you limit your interactivity logic to that expressible by a finite state machine with decidably halting transitions, congratulations, you are writing decidably halting programs, even though they don't "halt" in the temporal sense. It's always possible to tell whether they will halt for a given input by completely analyzing the state space.

[PKop]

Isn't this a question of upper-bound on input? Not specific examples that are less than the upper bound..