  The main aim of the paper is to give a short self-contained proof of the
decidability of language equivalence for deterministic pushdown automata, which
is the famous problem solved by G. Senizergues, for which C. Stirling has
derived a primitive recursive complexity upper bound. The proof here is given
in the framework of first-order grammars, which seems to be particularly apt
for the aim. An appendix presents a modification of Stirling's approach,
yielding a complexity bound of the form tetr(2,g(n)) where tetr is the
(nonelementary) operator of iterated exponentiation (tetration) and g is an
elementary function of the input size.
