What is a good example of an NL-complete context free language?
In other words, you are asked to find an $\rm NL$-complete language $A$ and a context-free language $B$ such that $A \equiv_{\rm{L}} B$. We choose $A = \it{PATH}$ and $\{{\tt{0}, \tt{1}， \tt{\#}}\}^* \supseteq  B = f(A)$, in which $f: A \to B$ is defined as follows.
    $$
\newcommand{\Bra}[1]{\langle #1 \rangle}
  f(\Bra{G, s, t}) = \Bra{s}^{\mathcal{R}}({\tt{\#}} \Bra{e_1} \Bra{e_2} \cdots \Bra{e_m} {\tt{\#}} )^n\Bra{t},
 $$
    where $G = (V, E)$, $|V| = n$, $E = \{e_1, \dots, e_m\}$, $\Bra{e_i} = {\tt{\#}}\Bra{u_i}{\tt{\#}}\Bra{v_i}^{\mathcal{R}{}}{\tt{\#}}$ if $e_i = (u_i, v_i)$.