"Source: Text/Group/GrpFP.text";
"Line: 11472";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpFP.text, line: 11472
// Example: H80E92 ()
print "Example: H80E92";
ei := GetEchoInput();
SetEchoInput(true);
F<a,b,c> := FreeGroup(3);
rels := [ a^4, b^2, (a,b)^3, (a*b)^8, ((a*b)^2*(a^-1*b)^3)^2, 
 c^2, (c*a*c*a^2)^2, (c*a)^3*(c*a^-1)^3,
 c*a*b*c*a^-1*b*a^-1*c*a*b*c*a^2*a*b*a^-1,
 c*a*b*c*b*a*c*a*c*a^-1*b*c*b*a^-1*c*a^-1,
 c*a*b*a^-1*c*a*b*a^-1*c*a*b*a^-1*c*a*b*a^-1,
 c*b*a^2*b*c*b*c*a^2*c*b*c*b*a^2*b,
 c*a^2*c*b*a*c*b*a*c*b*a*c*a^-1*c*a*b*a^-1,
 c*a^-1*b*a*c*a^-1*b*a*c*b*a*b*a^2*b*a^-1*b,
 c*a*b*a^-1*b*c*b*a^-1*b*c*a^-1*b*a*b*a*c*b*c*b,
 c*a*c*b*a*b*c*a*c*b*a*b*c*a*c*b*a*b,
 c*b*a^-1*b*c*a^-1*c*a^-1*b*a*b*c*b*c*a^2*b*a*b*a^-1,
 c*b*a^-1*b*a*b*c*b*a^-1*b*a*b*c*b*a^-1*b*a*b,
 c*a^2*b*a^-1*b*c*b*c*b*a^-1*b*a*c*b*a^2*b*a^-1*b
];
G<a,b,c> := quo< F | rels >;
S := sub< G | b, c*a*c*b*a*b >;
time Index(G, S);
assert $1 eq 114;
time R := Rewrite(G, S : Simplify := false);
NumberOfGenerators(R);
PresentationLength(R);
time ToddCoxeter(R, sub<R|> : Strategy := "Hard", Style := "C");
time Rs := Simplify(R);
NumberOfGenerators(Rs);
PresentationLength(Rs);
time Rsl := SimplifyLength(R);
NumberOfGenerators(Rsl);
PresentationLength(Rsl);
time ToddCoxeter(Rsl, sub<Rsl|> : Strategy := "Hard", Style := "C");
SetEchoInput(ei);
