  In a recent breakthrough result, Balliu et al. [FOCS'19] proved a
deterministic $\Omega(\min(\Delta,\log n /\log \log n))$-round and a randomized
$\Omega(\min(\Delta,\log \log n/\log \log \log n))$-round lower bound for the
complexity of the bipartite maximal matching problem on $n$-node graphs in the
LOCAL model of distributed computing.
  Both lower bounds are asymptotically tight as a function of the maximum
degree $\Delta$.
  We provide truly tight bounds in $\Delta$ for the complexity of bipartite
maximal matching and many natural variants, up to and including the additive
constant.
  As a by-product, our results yield a considerably simplified version of the
proof by Balliu et al.
  We show that our results can be obtained via bounded automatic round
elimination, a version of the recent automatic round elimination technique by
Brandt [PODC'19] that is particularly suited for automatization from a
practical perspective.
  In this context, our work can be seen as another step towards the
automatization of lower bounds in the LOCAL model.
