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Not sure what x^y^2 was supposed to be in your polynomial f.
Anyway, try something like this.
sage: R.<x,y> = PolynomialRing(ZZ, order='deglex')
sage: f = x^5 * y^2 + x^3 * y^2 - y + 1
sage: F = (x * y^2 - x, x - y^3)
sage: f.reduce(F)
x^5 + x^3 - y + 1
