We consider the computational complexity of several decidable problems about program schemes and simple programming languages. In particular, we show that the equivalence problem for Ianov schemes is NP-complete, but that the equivalence problem for strongly free schemes, which approximate the class of Ianov schemes which would actually be written, can be solved in time quadratic in the size of the scheme. We also show that many other simple scheme classes or simple restricted programming languages have polynomially complete equivalence problems. Some are complete for the same reason that Ianov schemes are complete and some are complete for other reasons.