This is a simple program:

- Given an input x, which is a positive integer.
- If x is even, assign x to be x/2, else assign x to be 3x + 1.
- Repeat step 2 if x > 1.

Conjecture: The program will always terminate for any input x.

Believe it or not? Try to prove or disprove it yourself.

And here is the JavaScript for the above program.