The realization space is
  [1   1   0                  x2 - 1   1   0    0    1         x1*x2 - x2 + 1                1    1]
  [0   1   1   -x1^2*x2 + x1*x2 - x1   0   0    1   x1   x1^2*x2 - x1*x2 + x1   x1*x2 - x2 + 1   x1]
  [0   0   0                       0   1   1   -1    1                  x1*x2               x2   x2]
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, x1 - 1, x2 - 1, x1, x1 + x2, x1 + x2 - 1, x1^2 + x2 - 1, x1^2*x2 - x1*x2 + x1 + x2 - 1, x1*x2 + 1, x1^2*x2 + x1*x2^2 - 2*x1*x2 + x1 + x2 - 1, x1*x2 - x2 + 1, x1 + 1, x1^2*x2 + x2 - 1]