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RDF (Resource Description Framework) is a standard language to represent graph databases. Query languages for RDF databases usually include primitives to support path queries, linking pairs of vertices of the graph that are connected by a path of labels belonging to a given language. Languages such as SPARQL include support for paths defined by regular languages (by means of Regular Expressions). A context-free path query is a path query whose language can be defined by a context-free grammar. Context-free path queries can be used to implement queries such as the "same generation queries", that are not expressible by Regular Expressions. In this paper, we present a novel algorithm for context-free path query processing. We prove the correctness of our approach and show its run-time and memory complexity. We show the viability of our approach by means of a prototype implemented in Go. We run our prototype using the same cases of study as proposed in recent works, comparing our results with another, recently published algorithm. The experiments include both synthetic and real RDF databases. Our algorithm can be seen as a step forward, towards the implementation of more expressive query languages.