LogTo("f5-3-a0.log");

LoadPackage("GBNP");

GBNP.ConfigPrint("y0","y1","y2","y3","y4");

s:=Indeterminate(Rationals,"L1");;
t:=Indeterminate(Rationals,"L2");;
u:=Indeterminate(Rationals,"L3");;

K:=[
[[[2,1],[1,3],[3,4],[4,2],[]],[1,1,1,1,-t]],
[[[3,1],[1,5],[5,2],[2,3],[]],[1,1,1,1,-t]],
[[[4,1],[1,2],[2,5],[5,4],[]],[1,1,1,1,-t]],
[[[5,1],[1,4],[4,3],[3,5],[]],[1,1,1,1,-t]],
[[[3,2],[2,4],[4,5],[5,3],[]],[1,1,1,1,-t]],
[[[1,1],[]],[1,-s]],
[[[2,2],[]],[1,-s]],
[[[3,3],[]],[1,-s]],
[[[4,4],[]],[1,-s]],
[[[5,5],[]],[1,-s]],
[[[1,2,1,2],[2,1,2,1],[1,2],[2,1],[]],[1,1,-t,-t,-u]]
];;

Print("Computing Grobner \n");

G:=SGrobner(K);

Print("1 is: \n");

PrintNP(StrongNormalFormNP([[[]],[1]],G));

Print("Hence the quotient is nonzero \n");