  We develop new computational methods for studying potential counterexamples
to the Andrews-Curtis conjecture, in particular, Akbulut-Kurby examples AK(n).
We devise a number of algorithms in an attempt to disprove the most interesting
counterexample AK(3). To improve metric properties of the search space (which
is a set of balanced presentations of the trivial group) we introduce a new
transformation (called an ACM-move here) that generalizes the original
Andrews-Curtis transformations and discuss details of a practical
implementation. To reduce growth of the search space we introduce a strong
equivalence relation on balanced presentations and study the space modulo
automorphisms of the underlying free group. Finally, we prove that
automorphism-moves can be applied to AK(n)-presentations. Unfortunately,
despite a lot of effort we were unable to trivialize any of
AK(n)-presentations, for n>2.
