The mu puzzle

So, recently i found a book called "Gödel, Escher, Bach: An Eternal Golden Braid" written by Douglas Hofstadter. Inside it, i read a very interesting puzzle that i decided to share with you.
The puzzle itsself is simple:
There is a system called the MIU-system. It utilises only 3 letters of the alphabet: M, I, and U.
This means that the only strings of this system are strings composed of these 3 letters.
For example:
String #1: MU
String #2: UIMI
String #3: UIIMUMIIUMUIM
et cetera, to strings of any length and letter combination.
Even though these are legitimate strings, the only string of letters you have available is MI. Using a set of rules shown below, you must alter this string, in order to create the final string : MU
When i use the letter x, it symbolises any possible string of letters. For example, MxI can be M followed by any number and combination of M, I, U.
The rules are the following:
~Rule #1:
If you possess a string whose last letter is I, you can add a U at the e…
The puzzle itsself is simple:
There is a system called the MIU-system. It utilises only 3 letters of the alphabet: M, I, and U.
This means that the only strings of this system are strings composed of these 3 letters.
For example:
String #1: MU
String #2: UIMI
String #3: UIIMUMIIUMUIM
et cetera, to strings of any length and letter combination.
Even though these are legitimate strings, the only string of letters you have available is MI. Using a set of rules shown below, you must alter this string, in order to create the final string : MU
When i use the letter x, it symbolises any possible string of letters. For example, MxI can be M followed by any number and combination of M, I, U.
The rules are the following:
~Rule #1:
If you possess a string whose last letter is I, you can add a U at the e…