The first step in the Cartan method is to express the pullback relation (1) in as invariant a way as possible through the use of a "prolongation". The most economical way to do this is to use a G-subbundle PM of the principal bundle of linear coframes LM, although this approach can lead to unnecessary complications when performing actual calculations. In particular, later on this article uses a different approach. But for the purposes of an overview, it is convenient to stick with the principal bundle viewpoint. The second step is to use the diffeomorphism invariance of the exterior derivative to try to isolate any other higher-order invariants of the G-structure. Basically one obtains a connection in the principal bundle PM, with some torsion. The components of the connection and of the torsion are regarded as invariants of the problem. The third step is that if the remaining torsion coefficients are not constant in the fibres of the principal bundle PM, it is often possible (although sometimes difficult), to normalize them by setting them equal to a convenient constant value and solving these normalization equations, thereby reducing the effective dimension of the Lie group G. If this occurs, one goes back to step one, now having a Lie group of one lower dimension to work with. The fourth step The main purpose of the first three steps was to reduce the structure group itself as much as possible. Suppose that the equivalence problem has been through the loop enough times that no further reduction is possible. At this point, there are various possible directions in which the equivalence method leads. For most equivalence problems, there are only four cases: complete reduction, involution, prolongation, and degeneracy. Complete reduction. Here the structure group has been reduced completely to the trivial group. The problem can now be handled by methods such as the Frobenius theorem. In other words, the algorithm has successfully terminated. On the other hand, it is possible that the torsion coefficients are constant on the fibres of PM. Equivalently, they no longer depend on the Lie group G because there is nothing left to normalize, although there may still be some torsion. The three remaining cases assume this. Involution. The equivalence problem is said to be involutive (or in involution) if it passes Cartan's test. This is essentially a rank condition on the connection obtained in the first three steps