In this paper some analogs of the Gröbner base for T-ideals are considered. A sequence of normal monomials of the T-ideal $T_2^{(3)}$ is built so that the monomials are independent w.r.t. the operation of monotonous substitution and the insertion operation. Also a theorem is proved stating that for algebras without $1$ a multilinear identity of the form $w_1[x_1,x_2]w_2$, where $x_1$, $x_2$ are variables and $w_1$, $w_2$ are monomials, belongs to every T-ideal that is finitely based w.r.t. the inclusion relation of the leading monomials.