A lexical analyzer uses the following patterns to recognize three tokens $T_1, T_2$, and $T_3$ over the alphabet $\{a, b, c\}$.
- $T_1: a?(b \mid c)^\ast a$
- $T_2: b?(a \mid c)^\ast b$
- $T_3: c?(b \mid a)^\ast c$
Note that ‘$x?$’ means $0$ or $1$ occurrence of the symbol $x.$ Note also that the analyzer outputs the token that matches the longest possible prefix.
If the string $bbaacabc$ is processed by the analyzer, which one of the following is the sequence of tokens it outputs?
- $T_1T_2T_3$
- $T_1T_1T_3$
- $T_2T_1T_3$
- $T_3T_3$