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 a single one of these systems might describe omitting types 1 and 2. However, we do not resolve whether it actually describes omitting mentioned types, but only prove that it implies this property, so this question is left for further examination.