$\mathit{ C}$-clones are polymorphism sets of so-called clausal relations, a special type of relations on a finite domain, which first appeared in connection with constraint satisfaction problems in [Creignou et al. 2008]. We completely describe the relationship w.r.t. set inclusion between maximal $\mathit{ C}$-clones and maximal clones. As a main result we obtain that for every maximal $\mathit{ C}$-clone there exists exactly one maximal clone in which it is contained. A precise description of this unique maximal clone, as well as a corresponding completeness criterion for $\mathit{ C}$-clones is given.
Categories: math.RA
