The algorithmic orientation-reversing symmetry problem for irreducible 3-manifolds

Let $M$ be a closed, orientable, irreducible $3$-manifold. Algorithmic orientation-reversing symmetry conjecture. There is an algorithm that determines whether $M$ admits an orientation-reversing self-homeomorphism. This problem is the remaining obstruction identified in the paper to deciding homeomorphism for all closed, orientable $3$-manifolds; the source does not state a resolution.