  The lambda Pi calculus can be extended with rewrite rules to embed any
functional pure type system. In this paper, we show that the embedding is
conservative by proving a relative form of normalization, thus justifying the
use of the lambda Pi calculus modulo rewriting as a logical framework for
logics based on pure type systems. This result was previously only proved under
the condition that the target system is normalizing. Our approach does not
depend on this condition and therefore also works when the source system is not
normalizing.
