Neil Hoffman and I are constructing polynomial-time verifiable certificates of non-hyperbolicity for nontrivial link exteriors (in closed orientable 3-manifolds), showing that hyperbolicity is in coNP for this class of compact 3-manifolds. By way of explanation, I will review crushing following Burton's new approach; survey the certificate literature for 3-manifolds; and give an algorithm for recognizing T2xI that fits on a napkin, which was the starting point of our work.