[GAP Forum] Checking equality of elements of words in a finitely presented group

[W. Edwin Clark]

I am trying to use GAP to establish equality of two words in a finitely
presented group and am having problems.

First here is a successful test case:

f:=FreeGroup(5);;
rel:=[(f.(5)*f.(1))^5];;
g:=f/rel;;
u:=GeneratorsOfGroup(g);;
(u[5]*u[1])^5 = Identity(g);  #testing this identity which is actually a
given relation works successfully

       true

But if I add some more relators to rel, I cannot even get
equality to the identity of the first relator.  Here's what I tried:

f:=FreeGroup(5);;
rel:=[(f.(5)*f.(1))^5];;
for i in [1..4] do
 Add(rel,(f.(i)*f.(i+1))*(f.(5)*f.(1))^(-1));
od;
rel;;
g:=f/rel;;
u:=GeneratorsOfGroup(g);

(u[5]*u[1])^5 = Identity(g);  #I gave up waiting for an answer

Why is this so difficult?

What I really want in this group is to show that

u[1]^5*u[2]*u[4]*u[1]*u[3]*u[5] = Identity(g)

Any help would be appreciated.

--Edwin Clark