The realization space is
  [0   1   1   x1 + 1   0   0               0   1   x1^2 + x1 - 1    1      x1^2 + x1 - 1]
  [1   0   1       x1   1   0              x1   1            x1^2    0               x1^2]
  [1   0   1       x1   0   1   x1^2 + x1 - 1   0   x1^2 + x1 - 1   x1   x1^3 + x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal with 1 generator
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1^2 + x1 - 1, x1^3 + x1^2 - 1, x1 + 1, x1^3 + x1^2 - 2*x1 + 1, 2*x1 - 1, 2*x1^2 - 1, x1^2 + 2*x1 - 2]