If a finite state machine is in a deadlock, i.e. a state that directly leads to itself no matter what, you trivially find the cycle. That is only a trivial exam

If a finite state machine is in a deadlock, i.e. a state that directly leads to itself no matter what, you trivially find the cycle. That is only a trivial example. Another example are programs that never jump backwards. There are many other functions where the halting problem is practically solveable. The question is, what are the problems that are impossible in a turing machine but practical in a real computer?