I simply translate his/her solution to eng, with proof omitted since i am lazy....:)

I didn't check the correctness carefully (due to the same reason...), but it seems to me it is correct.)

(1)

S[0]=0

S[i+1]=S[i]S'[i]

where S'[i] is the reversal of S[i].

(2)

alphabet={abcd}

S[0]=abcd

S[i+1] is obtained from S[i] by the following substitution :

a => abcd
b => acdb
c => adbc
d => acbd