Is there an infinite periodic sequence consisting of the letters $a$ and$ b$, such that if all letters are replaced simultaneously $a$ to $aba$ and letters $b$ to $bba$ does it transform into itself (possibly with a shift)? (A sequence is called periodic if there is such natural number $n$, which for every $i = 1, 2, . . . i$-th member of this sequence is equal to the ($i + n$)- th.)