  We describe a procedure which verifies that a group given by generators and
relators is word-hyperbolic. This procedure always works with a group which is
word-hyperbolic, provided there is sufficient memory and time devoted to the
problem. If the group is not word-hyperbolic, the procedure continues
indefinitely. We also describe a procedure which computes the thinness of
geodesic triangles in the Cayley graph of a word-hyperbolic group. Again this
procedure is bound to work, given sufficient memory and time.
