In [1,3] two strategies for Todd-Coxeter enumeration were described in detail. Felsch-Type methods try to extract as much information as possible from the relators and the current coset table and only define new cosets if necessary. HLT and look-ahead HLT, which will be refered to as HLT in the sequel, define as many new cosets as possible and only extract new information from the relators and the coset table if necessary.
If we compare our frameworks to these strategies, it can be seen that the original procedure follows the Felsch-Type methods and has the same drawbacks: extracting information is costly. The ''steps''- and the ''level''-framework are both similar to HLT: define a certain number of new cosets before extracting new information. The difference is that HLT uses some fixed sized table, i.e. the number of maximal definable cosets is fixed beforehand while our frameworks limit the number of newly defined cosets and the coset table, i.e. the ideal basis, is allowed to grow.
While the ''steps''-framework has a similar problem as HLT, that is, the number of cosets to be defined before extracting new information must be given before starting the computation, this is not the case for the ''level''-framework.