Hofstadter's MU Playground

Suppose there are the symbols M, I, and U which can be combined to produce strings of symbols. The MU puzzle asks one to start with the "axiomatic" string MI and transform it into the string MU using in each step one of the following transformation rules:

Rule 1
xI → xIU
Rule 2
Mx → Mxx
Rule 3
xIIIy → xUy
Rule 4
xUUy → xy
where x and y are variables that stand for any string in the language.

Can the puzzle be solved? Use this playground to answer the question! You will be presented with an interface displaying your goal (the string you should try to derive), your current string (the string you have), the derivation log (how you got there from the axiom) and the four rules above that you can apply to your current string to derive a new string. Sometimes a rule can be applied in multiple ways, and in such cases the playground will ask you to pick your path.

The reading for this section of the course is accessible online.

Ready? Pick a problem to get started: MIU, MUI, MIIII, MIIU, MIUI, MUUIU, MIIUIIU, MUUII, MUIIU, MUUIIUIIU, or attempt a random problem. If you feel up to it, give the MU puzzle a try.