We define a transformation from a left-linear constructor-based
conditional rewrite system into an overlapping inductively
sequential rewrite system.  This transformation is sound and
complete for the computations in the source system.  Since there
exists a sound and complete narrowing strategy for the target
system, the combination of these results offers the first
procedure for provably sound and complete narrowing computations
for the whole class of the left-linear constructor-based
conditional rewrite systems.
We address the differences between demand driven and lazy
strategies and between narrowing strategies and narrowing calculi.
In this context, we analyze the efficiency and practicality of
using our transformation for the implementation of functional
logic programming languages.  The results of this paper
complement, extend, and occasionally rectify, previously published
results in this area.