The realization space is
  [1   0   1         x1   1   0   x1^2 + x1 - 1   1         1        0         x1]
  [0   1   1   2*x1 - 1   0   0               0   1   -x1 + 1   x1 - 1   2*x1 - 1]
  [0   0   0          0   1   1     2*x1^2 - x1   1        x1      -x1       x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^10 - 3*x1^9 + 3*x1^8 + 3*x1^7 - 12*x1^6 + 13*x1^5 - 6*x1^4 + x1^3)
avoiding the zero loci of the polynomials
RingElem[x1, x1^2 + x1 - 1, x1 + 1, x1^4 + 2*x1^2 - 3*x1 + 1, x1 - 1, x1^3 + 2*x1^2 - 3*x1 + 1, 2*x1 - 1, x1^3 + 3*x1^2 - 4*x1 + 1, x1^2 - 4*x1 + 2]