  Given a sub-hyperbolic semi-rational branched covering which is not
CLH-equivalent a rational map, it must have the non-empty canonical Thurston
obstruction. By using this canonical Thurston obstruction, we decompose this
dynamical system in this paper into several sub-dynamical systems. Each of
these sub-dynamical systems is either a post-critically finite type branched
covering or a sub-hyperbolic semi-rational type branched covering. If a
sub-dynamical system is a post-critically finite type branched covering with a
hyperbolic orbifold, then it has no Thurston obstruction and is combinatorially
equivalent to a unique post-critically finite rational map (up to conjugation
by an automorphism of the Riemann sphere) and, more importantly, if a
sub-dynamical system is a sub-hyperbolic semi-rational type branched covering
with hyperbolic orbifold, we prove in this paper that it has no Thurston
obstruction and is CLH-equivalent to a unique geometrically finite rational map
(up to conjugation by an automorphism of the Riemann sphere).
