  We provide an algorithm for deciding simple grammar bisimilarity whose
complexity is polynomial in the valuation of the grammar (maximum seminorm
among production rules). Since the valuation is at most exponential in the size
of the grammar, this gives rise to a single-exponential running time.
Previously only a doubly-exponential algorithm was known. As an application, we
provide a conversion from context-free session types to simple grammars whose
valuation is linear in the size of the type. In this way, we provide the first
polynomial-time algorithm for deciding context-free session type equivalence.
