Toy example for the removal of inconsistencies. Removal of inconsistencies from a set of partial columns. On the left, the sites belonging to column "A" are denoted by a square box bearing that letter. On the right, the graph captures the immediate succession of the partial columns. The overall inconsistency can be detected by the cycle A→D→B→C→A. Assume that the DAG is obtained by removing the red edge C→A. The algorithm in section Getting an Acyclic Graph proceeds as indicated on the right. Namely, the longest path for each sequence is indicated with the bold black edges and the remaining edges from relation R are in grey. The result is the removal from the partial column "C" of the site indicated in red.