The realization space is
  [1   1   0                   x2^2   0   1   1        0                   x2^2    1              x2]
  [1   0   1   x1*x2^2 - x1*x2 + x1   0   1   0   x2 - 1   x1*x2^2 - x1*x2 + x1   x2   x2^2 - x2 + 1]
  [0   0   0                      0   1   1   1       x2                x1*x2^2   x2            x2^2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal with 2 generators
avoiding the zero loci of the polynomials
RingElem[x2, x2 - 1, x1 - x2, x1, x2^2 - x2 + 1, x1*x2^2 - x1*x2 + x1 - x2, 2*x2^2 - 2*x2 + 1, x1*x2 - x1 + x2, x1*x2^2 - x1*x2 + x1 - x2^2, x1 - x2^2, x1*x2^2 - x1*x2 + x1 - x2^3, 2*x1*x2^2 - 2*x1*x2 + x1 - x2^3, 2*x2 - 1, x1*x2^3 - 2*x1*x2^2 + 2*x1*x2 - x1 + x2^3, x1 + x2^2 - x2, 2*x1*x2^2 - x1*x2 + x1 - x2^2, x1 - 1, x1*x2^2 - x1*x2 + x1 + x2^2 - x2]