That would be an improvement, but still wouldn't be a solution.
At some point, we have to live with the fact that comparison in finitely
presented groups will only work reliably if we are lucky. What we can do is
try to make the set of "lucky" groups bigger. And at some point that will
come at the expense of time and/or memory.
But it would be definitely worth it to take advantage of what gap has
already done in that direction. But beware, their approach consists in
trying until it can prove that the elements are equal (or that they are not
equal). That means that if you are in one of the unlucky cases, just
comparing two elements will start to consume 100% of your cpu for the
eternity (or until the RAM is exhausted, whatever happens first).
If you want to play with a presentation with non decidable word problem,
you can try to paste this in a gap session:
F := FreeGroup("a","b","c","d","e","p","q","r","t","k");
a:=F.1;
b:=F.2;
c:=F.3;
d:=F.4;
e:=F.5;
p:=F.6;
q:=F.7;
r:=F.8;
t:=F.9;
k:=F.10;
G:=F/[p^10*a/(a*p), p^10*b/(b*p), p^10*c/(c*p), p^10*d/(d*p), p^10*e/(e*p),
q*a/(a*q^10), q*b/(b*q^10), q*c/(c*q^10), q*d/(d*q^10),
q*e/(e*q^10),r*a/r/a,r*b/r/b, r*c/r/c, r*d/r/d, r*e/r/e,
p*a*c*q*r/(r*p*c*a*q), p^2*a*d*q^2*r/(r*p^2*d*a*q^2),
p^3*b*c*q^3*r/(r*p^3*c*b*q^3), p^4*b*d*q^4*r/(r*p^4*d*b*q^4),
p^5*c*e*q^5*r/(r*p^5*e*c*a*q^5), p^6*d*e*q^6*r/(r*p^6*e*d*q^6),
p^7*c*d*c*q^7/(p^7*c*d*c*e*q^7), p^8*c*a*a*a*q^8/(r*p^8*a*a*a*q^8),
p^9*d*a*a*a*q^9*r/(r*p^9*a*a*a*q^9), p*t/p/t, q*t/q/t,
k*(a*a*a)^(-1)*t*(a*a*a)/(k/(a*a*a)*t*a*a*a )];
Then try to compare two elements of G.
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