  This article is a natural construction of our previous works. In this
article, we employ similar ideas due to MacLane to provide an estimate of
IC(K(X)|K,v) when (K(X)|K,v) is a valuation algebraic extension. Our central
result is an analogue of the estimate obtained in the valuation transcendental
case. We further provide a natural construction of a complete sequence of key
polynomials for v over K in the setting of valuation algebraic extensions.
