The first proof of the Dichotomy conjecture for conservative algebras (2003) introduced colored graphs of relational structures and suggested a very sophisticated solution algorithm for polynomial time problems. The alternative proof of the same result given by Barto in 2011 uses a different approach and presents a significantly simpler algorithm. In this talk we make use of recent developments in the CSP such as the Generalized MajorityMinority algorithm and Maroti’s reduction to simplify dramatically the old proof.