Thanks. This was asked on mathoverflow [1], you can win some points
if you paste it as an answer.

Adding a single linear equation break the efficiency, so your solution
appear to show that incremental groebner basis might be large.

[1]:  
https://mathoverflow.net/questions/463159/efficiency-of-groebner-basis-for-constraints-of-the-form-a-i-x-ib-ia-j-x-j

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