Homomorphism equivalence on etol languages†

Abstract
The following problems are shown to be decidable. Given an ETOL language L and two homomorphisms h 1 h 2is the length (Parikh vector) of h 1(x) and h 2(x) equal for each x in L? If Lis over a binary alphabet then we can also test whether h 1(x)= h 2(x) for each x in L.