Fig. 14

Example 2. a The \({\mathcal {H}}\)-tangle to be factorized. Circled numbers index all possible shrinkage locations for the lower hook \(2':7'\). b Apply the Heuristic for \({\mathcal {U}}\)-tangles. The dashed lines indicate the edges in the set \(I = \{2:2', 3:3'\}\). c Apply the Heuristic for \({\mathcal {U}}- tangles\) again. d The resulting \({\mathcal {T}}\)-tangle, it can be factorized optimally by using Algorithm 1