(*                          Ren-Cang Li, June 1, 1996
                            na.rcli@na-net.ornl.gov   *)

<<ReduceH

(* Possible Brackets *)
cmt[1]=Expand[Cmt[X,Cmt[X,Cmt[Y,Cmt[Y,Cmt[X,Y]]]]]];
cmt[2]=Expand[Cmt[X,Cmt[Y,Cmt[X,Cmt[Y,Cmt[X,Y]]]]]];
cmt[4]=Expand[Cmt[X,Cmt[Y,Cmt[Y,Cmt[X,Cmt[X,Y]]]]]];

cmt[3]=Expand[Cmt[Y,Cmt[Y,Cmt[X,Cmt[X,Cmt[X,Y]]]]]];
cmt[5]=Expand[Cmt[Y,Cmt[X,Cmt[Y,Cmt[X,Cmt[X,Y]]]]]];
cmt[6]=Expand[Cmt[Y,Cmt[X,Cmt[X,Cmt[Y,Cmt[X,Y]]]]]];

(* Results: The number of independent brackets:  2.
            The independent brackets are:
                cmt[1], cmt[2]. 
   Relations:

             cmt[3]                   = 0
            -cmt[2] +          cmt[4] = 0
            1/3 cmt[1]-cmt[2]+ cmt[5] = 0
            1/3 cmt[1]-cmt[2]+ cmt[6] = 0   *)

NumBrackets=6;
(* Do[{Print[cmt[i]];Pause[5]},{i,NumBrackets}]; *)

(* The maximum possible length of these vectors *)
MaxL=6!/(3! 3!);

<<ReduceT
