@L3viathan For Smallfuck, it's possible, since the tape is guaranteed to be finite. For F2, it's not possible, because there exist F2 programs of a finite length that halt, but that fact cannot be proven in a finite time. Such F2 programs will exist, regardless of how you try to solve the halting problem.
@Challenger5 You mean there are F2 programs that do not halt, and that cannot be proven, right? Any halting program can be proven to halt in finite time simply by running it. Or perhaps you mean for any given upper bound on run time, some halting programs will not halt in that time?
Discussion on question by Challenger5…
Discussion on question by Challenger5…