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  • $\begingroup$ The changing of the result is another bug that I do not understand. The result 0 is not expected to change for any ordering (because f is modeling an Abelian group multiplication). I have to enforce the condition f[i_, j_] /; i != j to get the correct result, which is usually unnecessary given the definition of f[i_, i_] already. I do not understand the behavior here either. $\endgroup$ Commented Nov 7, 2014 at 19:13
  • $\begingroup$ I think the only way to shed a bit of light is to analyze carefully Trace[] output. $\endgroup$ Commented Nov 7, 2014 at 19:44
  • $\begingroup$ I did looked into the Trace, but I did not gain much insight. It seems that the pairing process is not shown in the Trace output. $\endgroup$ Commented Nov 7, 2014 at 19:49