That means that words in the generators of the free group are not elements of the finitely presented group. Note that the relations are entered as relators , i.e., as words in the generators of the free group. You must not change the relators of a finitely presented group at all. The elements of a finitely presented group are words. There is one fundamental problem with this.
Different words can correspond to the same element in a finitely presented group.
Some set and group functions will not work correctly because of this problem . You should therefore only use the functions mentioned in Set Functions for Finitely Presented Groups and Group Functions for Finitely Presented Groups . Set Functions for Finitely Presented Groups 23.3. Group Functions for Finitely Presented Groups 23.4. Presentation Records 23.9.