Binary equality sets are generated by two words

We show that the equality set Eq(g,h) of two non-periodic binary morphisms g,h :A*→Σ* is generated by at most two words. If the rank of Eq(g,h)={α,β}* is two, then α and β begin and end with different letters. This in particular implies that any binary language has a test set of cardinality at most two.