1. Take a group for example. First we can set up a group G by

G:=<<a,b>|<a²=1,b³=1,(a.b)²=1>>. Actually,G=S₃. So how to simplify a long production,

such as "a.b.b.a.b.b.a.b"?

2. How to define a finitely presented algebra over some field, such as the enveloping algebra

or quantum group of a Lie algebra? And moreover how to do the similar computation about 

simplifying a long production?