  We give a method of constructing maps between tubular groups inductively
according to a set of strategies. This map will be a quasi-isometry exactly
when the set of strategies is consistent. Conversely, if there exists a
quasi-isometry between tubular groups, then there is a consistent set of
strategies for them.
  There is an algorithm that will in finite time either produce a consistent
set of strategies or decide that such a set does not exist. Consequently, this
algorithm decides whether or not the groups are quasi-isometric.
