Consider, for example, the "Hydra" cryptid (second in the list OOP linked).

This is a BB(2,5) machine (2 states, 5 symbols). There are other BB(2,5) machines that take more than 10↑↑4 steps to terminate. And the "Hydra" is called a cryptid because it might run even longer than that. So "naively" running it is unlikely to yield results before the heat death of the universe.

Of course, you can run it more cleverly by looking at what the machine is doing and essentially re-implementing this in a faster language. People have in fact done this, and simulated 4 million "fast" steps (corresponding to much more "naive" steps), and not found it to halt. If you want to run the simulation yourself, the code is on the website OOP linked, in the article about the Hydra.