Derived string

Alice has two non-empty strings, a string $S_1$ made up of lower case alphabets and another string $S_2$ which is binary consisting of only two characters $0$ and $1$. A string $S$ is called derived from two strings $a_0$ and $a_1$ with respect to a binary string $B$ if $S=a_{B_0}+a_{B_1}+a_{B_0}....+a_{B_i}+.....+a_{B_b}$, Where $b$ is the length of the binary string $B$ and $B_i$ is the $i^{th}$