A cellular automata experiment

These are the production rules from Douglas R. Hofstadter's book,
Gödel, Escher, Bach: An Eternal Golden Braid (see pages 259--262 of the 20th anniversary edition).
Using these, is it possible to transform MI to MU?

0: if the string ends in I, append U
1: if the string starts with M, copy the rest and append it (Mab -> Mabab)
2: if we have three I's in a row they become a U
3: two U's in a row are removed






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