Temporal interval algebra has generated strong interest for both theoretical and practical reasons. All its maximal tractable subalgebras (MTS) have been identified. Now is the time to make transition toward their practical applications. In this work we have proposed a formalism on how to classify an input temporal network in one of these MTSs, or decide its intractability. We have also proposed a linear algorithm for checking consistency when the input belongs to one of the seventeen MTSs, and for finding out the constraints responsible for inconsistency in case the network is unsatisfiable.