  In this work we focus on the convex feasibility problem (CFP) in Hilbert
space. A specific method in this area that has gained a lot of interest in
recent years is the Douglas-Rachford (DR) algorithm. This algorithm was
originally introduced in 1956 for solving stationary and non-stationary heat
equations. Then in 1979, Lions and Mercier adjusted and extended the algorithm
with the aim of solving CFPs and even more general problems, such as finding
zeros of the sum of two maximally monotone operators. Many developments which
implement various concepts concerning this algorithm have occurred during the
last decade. We introduce an unrestricted DR algorithm, which provides a
general framework for such concepts. Using unrestricted products of a finite
number of strongly nonexpansive operators, we apply this framework to provide
new iterative methods, where, \textit{inter alia}, such operators may be
interlaced between the operators used in the scheme of our \ unrestricted
\color DR algorithm.
