Deciding the existence of quasi weak near unanimity terms in finite algebras

We show that for a fixed positive integer k one can efficiently decide if a finite algebra A admits a k-ary weak near unanimity operation by looking at the local behavior of the terms of A. We also observe that the problem of deciding if a given finite algebra has a quasi Taylor operation is solvable in polynomial time by looking, essentially, for local quasi Siggers operations.
Comment: 17 pages, number n fixed to k in the proof of Lemma 11