The realization space is
  [1   1   0                -1   0   1   1    0                -1   x1 + 1       x1^2 + x1]
  [0   1   1   -x1*x2 + x1 - 1   0   0   1    1   -x1*x2 + x1 - 1        1   x1^2 + x1 - 1]
  [0   0   0                 0   1   1   1   x1               -x2       x1            x1^2]
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[x1, x1 - 1, x1*x2 - x1 + x2, x1^2*x2 - x1^2 - x2, x1^3*x2 - x1^3 + x2, x2, x1^3*x2 - x1^3 + x1^2*x2 - x1^2 + 1, x2 - 1, x1^2*x2 - x1^2 + 1, x1^2 + x1 - 1, x1^2*x2 - 2*x1^2 + 1, x1*x2 - x1 + 1, x1 + 1, x1^2*x2 - x1^2 + x1 - x2 + 1, x1^2*x2 - x1^2 + x1 + 1]