  Let G be a word-hyperbolic group with given finite generating set, for which
various standard structures and constants have been pre-computed. A
(non-practical) algorithm is described that, given as input two lists A and B,
each composed of m words in the generators and their inverses, determines
whether or not the lists are conjugate in G, and returns a conjugating element
should one exist. The algorithm runs in time O(m mu)$, where mu is an upper
bound on the lengths of elements in the two lists. Similarly, an algorithm is
outlined that computes generators of the centraliser of A, with the same bound
on running time.
