Searching for other a-2-free endomorphisms over 4 letters

© 2000 V. Keränen

All the endomorphisms below are a-2-free
for all a-2-free words over three letters {a,b,c}
(which exist up to length of seven).

Unfortunately, in these cases, it is not
possible to construct any appropriate
image word for the letter  d.

13 13 8

a -> abacabadacdbd
b -> acdcbcacbcdbd 
c -> abdbcdbd

15 15 9

a -> abacadabdadcdbd
b -> abacadcbcadcdbd
c -> abdbcbabd

15 15 25

a -> abcdbcacbdcdadb
b -> abcbdbadbdcdadb
c -> adacadabacbcdcadabacabadb