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\title{The Akra--Bazzi theorem and the Master theorem}
\author{Manuel Eberl}
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\begin{abstract}
This article contains a formalisation of the Akra--Bazzi method~\cite{akrabazzi} based on a proof by Leighton~\cite{leighton}. It is a generalisation of the well-known Master Theorem for analysing the complexity of Divide \& Conquer algorithms. We also include a generalised version of the Master theorem based on the Akra--Bazzi theorem, which is easier to apply than the Akra--Bazzi theorem itself.

Some proof methods that facilitate applying the Master theorem are also included. For a more detailed explanation of the formalisation and the proof methods, see the accompanying paper (publication forthcoming).
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