A lifted graph. (A) The lifted graph for the history graph in Figure 2(B). The blue and red lines represent, respectively, trivial and non-trivial lifted adjacencies. Similarly, the blue and red stars represent, respectively, trivial and non-trivial lifted labels. The free-roots are shown as a set of vertices above the other vertices, with a grey line identifying their matching branch-tree. (B) The module in (A) containing non-trivial lifted edges. Lower case letters are used to identify the sides..