Omitting unary and affine types

In this paper we examine the possibility of describing omitting types 1 and 2 by two at most ternary terms and any number of linear identities. All possible cases of systems of linear identities on two at most ternary terms are being analyzed, and it is shown that only three of these systems might describe omitting types 1 and 2. However, we do not resolve whether either of them actually describes omitting mentioned types, but only prove that each of them implies this property, so this question is left for further examination.