if the starting string has 2 digits, it is either 2 times the same digit or 2 different digits.
In this case there will be either 1 2 in the sequence or 2 1
If there is 1 2, then the third string will be 0010000
Starting to the fourth one, the sequences will be 0100000000 (1 1 and 0 other digits) all the time therefore it repeats....
If there are 2 1, then the third sequence will be 0200000000
then the fourth :0010000000
Starting to the fifth, the sequences will always be 0100000000 therefore it repeats.
In conclusion, the sequences repeats after the 5th sequence for any 2 digits initial sequence.