In this paper we describe the architecture of ARQo, a first approach for SPARQL static query optimization in ARQ. Specifically, we focus on static optimization of BasicGraphPattern (BGP) for in-memory models. Static query optimization is intended as a query rewriting process where the set of triple patterns defined for a BGP are rewritten according to a specific order. We propose a rewriting process according to the estimated execution cost of joined triple patterns in increasing order. Specifically, the estimated execution cost is a function of multiple parameters such as the estimated selectivity of joined triple patterns, the availability of indexes or pre-calculated result sets. 10 Pages