Modeling relation paths has offered significant gains in embedding models for knowledge base (KB) completion. However, enumerating paths between two entities is very expensive, and existing approaches typically resort to approximation with a sampled subset. This problem is particularly acute when text is jointly modeled with KB relations and used to provide direct evidence for facts mentioned in it. In this paper, we propose the first exact dynamic programming algorithm which enables efficient incorporation of all relation paths of bounded length, while modeling both relation types and intermediate nodes in the compositional path representations. We conduct a theoretical analysis of the efficiency gain from the approach. Experiments on two datasets show that it addresses representational limitations in prior approaches and improves accuracy in KB completion.