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