# Takes a tape representing a natural number k (see Boolos, Burgess
# and Jeffrey for definition) and returns a tape representing a pair
# <k,k>.

0 1 _ r 1
0 _ _ r 99
1 _ _ r 2 # Look for blank
1 1 1 r 1
2 _ 1 r 3 # Wrote my 1.
2 1 1 r 2
3 _ _ r 4
3 1 _ r 5
4 _ 1 l 6
5 _ 1 r 7
5 1 1 4 5
6 _ _ l 8
6 1 1 l 6
7 _ 1 l 6
8 _ _ l 9
8 1 1 l 8
9 _ _ r 0
9 1 1 l 9