# This is the 3 generator Engel-4 group of exponent 5 from Tom Litt's
# thesis.  Note that there are free reductions in, eg, [a,ab,ab,ab,ab].

Gr: a,b,c;
Rel:
  [a,b],

  [c,a,a,a], [c,a,a,c], [c,a,c,a], [c,a,c,c],
  [c,b,b,b], [c,b,b,c], [c,b,c,b], [c,b,c,c],

  [c,a,a,b,b], [c,b,b,a,a], [c,a,c,b,b], [c,b,c,a,a],

  (a)^5, (b)^5, (c)^5, (ab)^5, (aB)^5, (ac)^5, (aC)^5, (bc)^5, (bC)^5,
  (abc)^5, (abC)^5, (aBc)^5, (aBC)^5, (abcc)^5, (abbc)^5, (abbcc)^5,
  (aBcc)^5, (abbC)^5, 

  (A)^5, (aab)^5, (aac)^5, (bbc)^5, (aaB)^5, (aaC)^5, (bbC)^5, (Abc)^5,
  (ABc)^5, (AbC)^5, (ABC)^5, 

  (Abcc)^5, (Abbc)^5, (Abbcc)^5, (ABcc)^5, (aBBc)^5, (aabc)^5, (aabC)^5,
  (aaBc)^5, (aaBC)^5, (aabcc)^5, (aabbc)^5, (aaBcc)^5, (aabbC)^5, 

  [a,c,c,c,c], [A,c,c,c,c], [a,C,C,C,C], [A,C,C,C,C],
  [b,c,c,c,c], [B,c,c,c,c], [b,C,C,C,C], [B,C,C,C,C],

  [c,a,a,a,a], [C,a,a,a,a], [c,A,A,A,A], [C,A,A,A,A],
  [c,b,b,b,b], [C,b,b,b,b], [c,B,B,B,B], [C,B,B,B,B],

  [a,ac,ac,ac,ac], [a,AC,AC,AC,AC], [b,bc,bc,bc,bc], [b,BC,BC,BC,BC],

  [c,ac,ac,ac,ac], [c,AC,AC,AC,AC], [c,bc,bc,bc,bc], [c,BC,BC,BC,BC]
  ;
Gen: ab,bc;

Wo:4M;
Mess:10000;
Hard;