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It works like this:
The cleartext is converted to encrypted form by changing every letter to the one 13 later than it in the alphabet. For the purpose of the assignment you are to assume that the alphabet is circular, rather than linear like you were taught in primary school. It's like using a decoder-ring from the cereal box (see the picture to the right to get some idea of what I mean if your cereal never came with prizes). So the song would go like "...xyzabcdefg..." Repeating the process recovers the original text, because each letter is rotated around to its original value.
Because the rot13 encryption standard originated in the hard world of Usenet, a variety of other solutions exist for comparison. Headquarters insists on a fresh implementation, but the Jargon File has details that you may find historically interesting.
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