  This paper gives a proof that the fundamental group of a class of closed
orientable 3-manifolds constructed from three injective handlebodies has a
solvable word problem. This is done by giving an algorithm to decide if a
closed curve in the manifold is null-homotopic. Non-Haken and non-Seifert
fibered examples are constructed by performing Dehn surgery on a class of
two-bridge knots.
