User blog comment:LittlePeng9/Random Turing machines/@comment-5150073-20130410080930

Your power calculator, like arbitrary root extractor, has some problem: it doesn't work for n=0,1 and 2. I believe that for n=0, you can just add a few rules:

0 _ * r 19

19 1 _ r 19

19 _ 1 r halt

For n=1, you can just initially check whether the power is 1 or not. I propose the following rules:

0 1 * r 20

0a 1 * l 0a

20 1 * l 0a

20 _ * l 21

21 1 _ l halt