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A marked free monoid morphism is a morphism for which the image of eachgenerator starts with a different letter, and immersions are the analogous mapsin free groups. We show that the (simultaneous) PCP is decidable for immersionsof free groups, and provide an algorithm to compute bases for the sets, calledequalisers, on which the immersions take the same values. We also answer aquestion of Stallings about the rank of the equaliser.  Analogous results are proven for marked morphisms of free monoids.

The Post Correspondence Problem and equalisers for certain free group and monoid morphisms