Let D be the graded Q vector space generated by motivic multiple zeta values modulo “π^2”. The depth filtration is defined as the subspaces of D generated by MZV's whose lengths are less than or equal to given numbers. Broadhurst and Kreimer gave a conjecture on the two variable generating function of the dimensions of weight n and depth d part. This conjecture suggests the existence of an influence of mixed elliptic motives on mixed Tate motives. The Hopf algebra classifying the mixed elliptic motives is given by the relative bar complex defined by Hain. In this talk, we introduce a certain resolution, called a sandwich resolution of a dual free associative algebra motivated by the Broadhurst-Kreimer's generating function and the relative bar complex.