Conversion to a Finitely Presented Group

There is a standard way to convert an automatic group into a finitely presented group using the function Relations. This is shown in the following example.

Example GrpAtc_Conversion (H31E9)

> FG<a,b,c> := FreeGroup(3);
> Q := quo< FG | a^-1*b*a=b^2, b^-1*c*b=c^2, c^-1*a*c=a^2>;
> G := AutomaticGroup(Q);
> print G;
A confluent automatic group.
Generator Ordering = [ a, a^-1, b, b^-1, c, c^-1 ]
The first word difference machine has 1 state.
The second word difference machine has 1 state.
The word acceptor has 1 state.
The word multiplier has 1 state.
> P<x,y,z> := quo< FG | Relations(G) >;
> print P;
Finitely presented group P on 3 generators
Relations
    z = Id(P)
    y^-1 = Id(P)
    x^-1 = Id(P)
    x = Id(P)
    z^-1 = Id(P)
    y = Id(P)