This is the symmetry group of the icosahedron.  We demonstrate how we can reduce a word in the group using NCSimplifyAll.  The group has 3 nontrivial defining relations, and we reduce the commutator to the fifth power minus one.   NCSimplifyAll is a command that reduces the first arguement using the rules in the second arguement, with the number of iterations specified in the third arguement.

First you must load in NCGB with the following command

<< NCGB.m

This does not take into account your path to the NC directory.   Therefore, you may have to change this command.

SNC[r, f, Inv[r], Inv[f]]

SetMonomialOrder[{r, f, Inv[r], Inv[f]}]

NCSimplifyAll[{
        r**f**Inv[r]**Inv[f]**r**f**Inv[r]**Inv[f]**r**f**Inv[r]**Inv[f]**r**
            f**Inv[r]**Inv[f]**r**f**Inv[r]**Inv[f] - 1}, {
        r**r**r**r**r -> 1, f**f -> 1, r**f**r**f**r**f -> 1, Inv[f]**f -> 1, 
        f**Inv[f] -> 1, Inv[r]**r -> 1, r**Inv[r] -> 1}, 4]

The answer is 0, meaning that the commutator raised to the fifth power is equal to 1 in the group.