According to aristotle democracy was the best type of rule

This is complicated. He believed that democracy brings about a clash between the classes which ends with despotism. He did not like it, but instead supported what he called a polity. Now, polity is similar to today's democracy, but different from old democracy. So, he did think that the best way is democracy (the one existing now) but did not think that the ancient democracy was a great type of rule.

 Unfortunately, the answers given above are incorrect. Aristotle was a student of Plato, who himself loathed democracy, because the democratic assembly of Athens condemned Socrates to death. Aristotle himself fell victim to the same assembly and was banished from Athens. He too was no friend of democracy. 

In "The Politics," as you rightly point out, Aristotle listed the three most prevalent forms of government and stated that each, left to its own devices, would degenerate: Monarchy to Tyranny, Aristocracy to Oligarchy, and Democracy to Anarchy. Thus, Aristotle did not choose one form as being superior to the others, and instead offered that a superior form would be one which incorporated all three. 

Although he never explicitly stated it, Aristotle was arguing for the later idea of "Checks and Balances" and "Separation of Powers." His writings had a profound impact on the French political philosopher Montesquieu whose 1752 classic "The spirit of laws" argues for political stability through separation of powers in government. And Aristotle's and Montesquieu's work had an even more profound influence on James Madison, the principal architect of the American Constitution. 

The ultimate form of the American government was virtually taken from these writings, as Madison and the other founders created a government of Checks and Balances based on the three-fold division of Aristotle: 

Monarchy = The Presidency. 
Aristocracy = The Senate (and to a lesser extent, the Judiciary). 
Democracy = The House of Representatives. 

That the American government has lasted as long as it has, and has produced (more or less) limited government vindicates Aristotle's beliefs.