The ''level''-framework which is implemented by Procedure 3 (see page ) is independent of such a value. Instead of a fixed number supplied by the user, an internal condition triggers the Gröbner basis computation.
At the beginning only the letters of the alphabet are added to the border set . This is called level 1. Each element selected from the border set which is a new coset is added to the coset-set . Further, it is multiplied with all letters of the alphabet except the inverse of its last letter. These Elements have length 2 and are added to the new border set . Finally, the multiplication table is extended. If the current border set is empty the new border set becomes current and the Gröbner basis computation is performed. Thus, the border set of level consist of all elements of length which were generated by the previous level . They are examined before the Gröbner basis of is computed again. As the recomputation of the Gröbner basis is triggered by the procedure itself this framework is self-adapting with respect to the number of new cosets defined.
As all elements of the current level are considered before the recomputation of , that is all elements of length , this method is independent of the order in which these elements are considered. Nevertheless, this framework, too, still depends on the method used to select elements from the borderset.