Fig. 5

Shown is a binary and biologically feasible gene tree \((T;t,\sigma )\) (center) that is obtained as the observable part of the true scenario (left). However, there is no reconciliation map for \((T;t,\sigma )\) to any species tree according to Def. 2 because \(\mathcal {S}(T;t,\sigma )\) is inconsistent. Nevertheless, a relaxed reconciliation map \(\mu\) between \((T;t,\sigma )\) and the species tree exists (right). However, this map does not satisfy Lemma 4.2(2) since \(\mu (a')=A\) and \(\mu ({\text {lca}}_{T_{\mathcal {\overline{E}}}}(b',c'))\) are comparable. See text for further details