The realization space is
  [1   x1^2 + 1   1   x1^2 + 1   0   0          0   x1^2 + 1   x1^2 + 1    1]
  [1         x1   0         x1   1   0         x1          1          1    1]
  [1         x1   0   x1^2 + 1   0   1   x1^2 + 1         x1          0   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal with 1 generator
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1^3 - 2*x1^2 + x1 - 1, x1^2 + 1, x1^2 - x1 + 1, x1^3 - x1^2 + 2*x1 - 1]