The realization space is
  [1   1         1   0   1   0     x1 - 1         1      x1 - 1    1                  0]
  [0   1   -x1 + 1   1   0   0          0   -x1 + 1   x1^2 - x1    1    x1^2 - 2*x1 + 1]
  [0   0         0   0   1   1   2*x1 - 1        x1    2*x1 - 1   x1   -x1^2 + 3*x1 - 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (4*x1^11 - 28*x1^10 + 73*x1^9 - 86*x1^8 + 36*x1^7 + 16*x1^6 - 22*x1^5 + 8*x1^4 - x1^3)
avoiding the zero loci of the polynomials
RingElem[x1^3 - x1^2 - 2*x1 + 1, x1, 2*x1 - 1, x1 - 2, x1^2 - 3*x1 + 1, x1 - 1, x1^2 - 4*x1 + 2, x1^2 + 2*x1 - 1]