Term Satisfiability Problem for Two-Element Algebras is in QL or is NQL-Complete

We show that the term satisfiability problem for finite algebras is in NQL.Moreover we present a complete classification of the computational complexity of the term satisfiability problem for two-element algebras. We show that for any fixed two-element algebra the problem is either in QL or NQL-complete. We show that the complexity of the considered problem, parameterized by an algebra, is determined by the clone of term operations of the algebra.