  We present a solution to the conjugacy decision problem and the conjugacy
search problem in Garside groups, which is theoretically simpler than the usual
one, with no loss of efficiency. This is done by replacing the well known
cycling and decycling operations by a new one, called cyclic sliding, which
appears to be a more natural choice.
  We give an analysis of the complexity of our algorithm in terms of
fundamental operations with simple elements, so our analysis is valid for every
Garside group. This paper intends to be self-contained, not requiring any
previous knowledge of prior algorithms, and includes all the details for the
algorithm to be implemented on a computer.
