  This paper starts the Wilf-classification of mesh patterns of length 2.
Although there are initially 1024 patterns to consider we introduce automatic
methods to reduce the number of potentially different Wilf-classes to at most
65. By enumerating some of the remaining classes we bring that upper-bound
further down to 56. Finally, we conjecture that the actual number of
Wilf-classes of mesh patterns of length 2 is 46.
