We give a combinatorial proof of a theorem first proved by Souto which
says the following. Let M1 and M2 be simple 3–manifolds with
connected boundary of genus g>0. If M1 and M2 are glued via a
complicated map, then every minimal Heegaard splitting of the
resulting closed 3–manifold is an amalgamation. This proof also
provides an algorithm to find a bound on the complexity of the gluing
map.
