  We develop tools for classification of contraction algebras and apply these
to solve the problem on classification up to isomorphism of 8 and 9 dimensional
algebras corresponding to 3-fold flops. We prove that there is only one up to
isomorphism contraction algebra of dimension 8, and two algebras of dimension
9. The formulae for the dimension of algebra, depending on the type of the
potential are obtained. In the second part of the paper we show that associated
graded structure to brace and truss with appropriate descending ideal
filtration is pre-Lie.
