  The equaliser of a set of homomorphisms $S: F(a, b)\rightarrow F(\Delta)$ has
rank at most two if $S$ contains an injective map, and is not finitely
generated otherwise. This proves a strong form of Stallings' Equaliser
Conjecture for the free group of rank two.
  Results are also obtained for pairs of homomorphisms $g,
h:F(\Sigma)\rightarrow F(\Delta)$ when the images are inert in, or retracts of,
$F(\Delta)$.
