In our set-theoretical setting, a relation R on X is called consistent if all restrictions of the tansitive closure of the union ≤ ∪ R to the idividual sequences coincides with their respective 'natural' linear orderings. With the weak version of our anchored-alignment approach, we are looking for an alignment Ali wich maximum score such that the union Ali ∪ Anc is consistent. With the strong option, we are looking for a maximum-scoring alignment Ali that is a superset of Anc. With both program options, our optimisation problem is to find an alignment Ali with maximum score – under the additional constraint that the set-theoretical union Ali ∪ Anc is consistent. In the weak anchoring approach, the output alignment is Ali while with the strong option, the program returns the transitive closure of the union Ali ∪ Anc.