Question: Elimination orders?

Hello! I have an ideal in 12 variables. I wish to eliminate the last four. I did:

ord := lexdeg([x[9],x[10],x[11],x[12]], [x[1],...,x[8]]);

gb_myI := Basis(myI, ord);


However, the resulting Grobner basis had all 12 variables. Did I misapply the lexdeg? Or perhaps I don't quite understand the eliminnation order?

Any help or comments would be appreciated!




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