In the proof of Theorem 4.3 and Theorem 4.5 of our paper Bumpless pipe dreams meet puzzles, we reduce the varification of Yang--Baxter equations to finite cases when \(k=3\) and \(a_1,a_2,a_3,b_1,b_2,b_3\in \{0,1,2,\ldots,6\}\) with \(\#\{a_1,a_2,a_3,b_1,b_2,b_3\}\leq 3\). Here we present the code varifying them.
Note: The code above will time out after 1 minute when run online. To fully execute the code, it should be run in SageMath.