PIE-DAGs can also be constructed upwards from the lowest-order fragments, as illustrated in Fig. . This process begins by including all primary fragments in the graph, whereupon dimers are added if they meet the screening criteria. In the hypothetical example of Fig. , dimers AD and BD are determined to be negligible, as they were in the corresponding top-down example of Fig. (a). Trimers and higher-order fragments are added subsequently, with the constraint that in order for a new node (representing a non-negligible subsystem) to be added, all of its parents must exist already within the PIE-DAG, meaning that each parent must be non-negligible according to the screening criteria. Under these conditions, the nodes ABD, ACD, and BCD are not considered for addition to the scheme in Fig. , meaning that they are not even tested with the low-level screening method. The node ABC (depicted in yellow), is considered and ∆E low ABC is evaluated; this trimer will be included in the scheme if and only if it satisfies the threebody screening criteria, meaning Eq. ( ) in the present implementation.