X := "xyt";
Ordering := "LLEX";
R := [];
F1 := [[1,"xx"], [-1,"yx"]];
F2 := [[1,"xy"], [-1,"ty"]];
F3 := [[1,"xt"], [-1, "tx"]];
F4 := [[1,"yt"], [-1, "ty"]];
F := [F1, F2, F3, F4]; --F=(xx-yx, xy-ty, xt-tx, yt-ty)
NC.MRBP(X, Ordering, R, F);
[[[1, "yt"], [-1, "ty"]], [[1, "xt"], [-1, "tx"]], [[1, "xy"], [-1, "ty"]],
[[1, "xx"], [-1, "yx"]], [[1, "tyy"], [-1, "tty"]], [[1, "yyx"], [-1, "tyx"]],
[[1, "ttyy"], [-1, "ttty"]], [[1, "tyyx"], [-1, "ttyx"]]]
-------------------------------
X := "xyt";
Ordering := "ELIM";
R := [];
F1 := [[1,"xx"], [-1,"yx"]];
F2 := [[1,"xy"], [-1,"ty"]];
F3 := [[1,"xt"], [-1, "tx"]];
F4 := [[1,"yt"], [-1, "ty"]];
F := [F1, F2, F3, F4]; --F=(xx-yx, xy-ty, xt-tx, yt-ty)
NC.MRBP(X, Ordering, R, F);
[[[1, "yt"], [-1, "ty"]], [[1, "tyy"], [-1, "tty"]], [[1, "ttyy"], [-1, "ttty"]],
[[1, "xt"], [-1, "tx"]], [[1, "xy"], [-1, "ty"]], [[1, "yyx"], [-1, "tyx"]],
[[1, "tyyx"], [-1, "ttyx"]], [[1, "xx"], [-1, "yx"]]]
-------------------------------
X := "xyz";
Ordering := "LLEX";
R := [];
F1 := [[1,"xy"], [-1,"z"]];
F2 := [[1,"yz"], [-1,"x"]];
F3 := [[1,"zx"], [-1, "y"]];
F := [F1, F2, F3]; -- F=(xy-z, yz-x, zx-y)
NC.MRBP(X, Ordering, R, F);
[[[1, "zx"], [-1, "y"]], [[1, "yz"], [-1, "x"]], [[1, "yy"], [-1, "zz"]],
[[1, "xy"], [-1, "z"]], [[1, "xx"], [-1, "zz"]], [[1, "zzz"], [-1, "yx"]],
[[1, "zzy"], [-1, "xz"]], [[1, "yxz"], [-1, "zyx"]], [[1, "xzz"], [-1, "zy"]],
[[1, "xzy"], [-1, "yxz"]]]
-------------------------------
X := "xyz";
Ordering := "ELIM";
R := [];
F1 := [[1,"xy"], [-1,"z"]];
F2 := [[1,"yz"], [-1,"x"]];
F3 := [[1,"zx"], [-1, "y"]];
F := [F1, F2, F3]; -- F=(xy-z, yz-x, zx-y)
NC.MRBP(X, Ordering, R, F);
[[[1, "zzzzz"], [-1, "z"]], [[1, "zyz"], [-1, "y"]], [[1, "yzz"], [-1, "zzy"]],
[[1, "zzzy"], [-1, "yz"]], [[1, "yy"], [-1, "zz"]], [[1, "yzy"], [-1, "z"]],
[[1, "yyz"], [-1, "zyy"]], [[1, "yyy"], [-1, "yzz"]], [[1, "x"], [-1, "yz"]]]
-------------------------------
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