Two schema problems from the 1970s are examined, monadic recursion schemes and first-order recursion schemas. Research on these problems halted because they were shown to be equivalent to the problem of decidability of language equivalence between DPDA (deterministic pushdown automata). Recently a decidability proof for equivalence of DPDA was given by Sénizergues [10, 11], which therefore also solves the schema problems. However Sénizergues proof is quite formidable. A simplification of the proof was presented by the author  using ideas from concurrency theory (for showing decidability of bismilarity [9, 12]) and crucial insights from Sénizergues’s intricate proof. In this abstract we concentrate on first-order schemes and we outline a solution, based on the DPDA equivalence proof, which is reasonably close to its original formulation. We make use of Courcelle’s work [1, 2], which shows how to reduce this schema problem to decidability of language equivalence between strict deterministic grammars. And the proof in  of decidability of DPDA equivalence proceeds via (a small extension of) these grammars.