HOW TO CREATE A GAME?

In this game, You are given only three alphabets M,I,U. That means, the following are the only valid strings.
MU
UIM
MUUMUU

Rules of the game
1. If you possess a string whose last better is I. You can add on a U at the end.

2. Suppose you have Mx. Then you may add Mxx to your collection. 'x' being string in the system.
Examples:
From MIU, you may get MIUIU
from MU, you may get MUU
From MUM you may get MUMUM

3. If III occurs in one of the strings in your collection, you may make a new string with U in place of I1I.
Examples:
From UMIIIMU, you can make UMUMU
From MIIII, you can make MIU

4. If UU occurs inside one of your strings, you can drop it.
From UUU get U
From MUUUIII, get MUIII

At any point, you can apply any rule which you think as the best for the given situation.

Goal: Produce MU from the starting string MI using the above rules.
Can you make it? What rule, you want to modify or add, in order to make the game more interesting and achievable.
The way you play the game make it as an art.

Suppose, I want to produce the string MUIIU, How to go about?
1. MI starting string
2. MII by rule 2
3. MIIII by rule 2
4. MIIIIU by rule 1
5. MUIU by rule 3
6. MUIUUIU by rule 2
7. MUIIU by rule 4

We got it. This is how the mathematics, a game, computer program or a puzzle works.
Play this game or create your own game. Have fun?
By the way, this puzzle is taken from the book 'Godel, Escher, Bach', a Pulitzer prize winner.

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