“…A similar characterization exists for bounded width via wnu identities of all arities ≥ 3 [6] and some other identities [41]. For templates within the range of Conjecture 1.6, it is believed that membership in P can be described by the local (i.e., on all finite subsets of the domain) satisfaction of non-trivial nonnested identities [3], [4], [7], [35], [36], since this condition obstructs the most obvious reason for NP-hardness, namely the pp-construction of an NP-hard finite template. The condition implies the global satisfaction of the (slightly nested) pseudo-Siggers identity e•s(x, y, x, z, y, z) = f •s(y, x, z, x, z, y) [8], [9].…”