  Recently, Li et al. [2022] presented a dynamic Dyck-reachability algorithm
for bidirected graphs. The basic idea is based on updating edge weights in a
data structure called the merged graph $G_m$. As noted in Krishna et al.
[2023], the edge deletion procedure described in the algorithm of Li et al.
[2022] cannot properly update the weights in the presence of cycles in $G_m$.
This note discusses the cycle case and the time complexity.
