Word Game - Just for Fun

Years ago I invented a word game. It involves the letters of a word and rearrangements.

The rule is: you start with a word, say like abc. Then you rearrange by the rule
abc -> bca -> cab
All must be words. Example:
tea -> eat -> ate
I could find only three such three-letter words, and one is a stretch. The first is "tea," the second is "spa," and the third is "one." Therein lies the stretch: eon -> one -> neo. "Neo" is kind of a word.

I never could find a four letter word, abcd, wherein
abcd ->bcda -> cdab -> dabc are all words. Can you?
Well, if you wish to stretch real words a bit, try "haha" -> "ahah" and so on. You know both words, the second is one of those a-hah moments.

I can find four-letter words where there are four rearrangements of the letters, each making words.
Example: team -> meat -> mate -> tame
There are others. This is not truly a problem.

Word of caution... I've been hooked for years, but never got beyond what you see.

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