The realization space is
  [1   x1 + 1        1   1   0        1   0   x1    x1^2 + x1              0    1]
  [1       x1        0   0   1       x1   0   x1         x1^2           x1^3   x1]
  [0   x1 + 1   x1 + 1   0   0   x1 + 1   1   x2   x1*x2 + x2   x1^2*x2 - x2   x2]
in the multivariate polynomial ring in 2 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x2, x1^2 + x1 - 1, x1 - x2, x1 + 1, x1^3 + x1^2 - x2, x1 - 1, x1 - x2 + 1, x1, x2 - 1, x1^2 + x2 - 1, x1^3 - x1^2*x2 + x1*x2 - x2, x1^4 + x1^3 - x2, x1^4 - x1^3*x2 + x1^3 + x1*x2 - x2, x1^3 - x1^2*x2 + 2*x1*x2 - x2, x1^2 - x1*x2 + x2, x1^3 + x1*x2 - x2, x1^2 + x1 - x2, x1*x2 + x1 - x2]