  In 1985, Bucher, Ehrenfeucht and Haussler studied derivation relations
associated with a given set of context-free rules. Their research motivated a
question regarding homomorphisms from the semigroup of all words onto a finite
ordered semigroup. The question is which of these homomorphisms induce a well
quasi-order on the set of all words. We show that this problem is decidable and
the answer does not depend on the homomorphism, but it is a property of the
ordered semigroup.

Formal Languages and Automata Theory