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Especially if you are concerned about performance you should never create univariate polynomial rings over univariate polynomial rings. Directly using multivariate polynomial rings will be much faster.

Bonus: its then easy to substitute other variables since all variables are treated at the same level, for example:

sage: S1.<x1,y1> = ZZ[]
sage: S2.<y2,x2> = ZZ[]
sage: p1 = y1*x1 + y1
sage: p1(y2,x2)
y2*x2 + x2