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