gap> k:=20;;rels:=[x^2,x*y^k*x^-1*y^(-1-k)];;D:=F/rels;;
gap> R:=ResolutionSmallGroup(D,7);;
gap> List([0..7],R!.dimension);
[ 1, 2, 2, 2, 2, 2, 2, 2 ]
