If we can write a program that translates said arbitrary program into the rules for an n-state, m-symbol turing machine, where n = (2|3|4|5) and m = 2, then yes

If we can write a program that translates said arbitrary program into the rules for an n-state, m-symbol turing machine, where n = (2|3|4|5) and m = 2, then yes - we can determine if the program terminates or not. We can make some fuzzy guesses whether or not the program terminates or not in other state/symbol combinations. http://en.wikipedia.org/wiki/Busy_beaver http://en.wikipedia.org/wiki/Busy_beaver If we ever did write said program that could determine whether any /arbitrary/ program is infinite, then we have solved the halting problem. And that would be quite something.