The realization space is
  [1   1   x1 - 1   0   0   1    1            x1 - 1         0         1         1]
  [0   1       -1   1   0   0    1                -1    x1 - 2   -x1 + 2   -x1 + 2]
  [0   0        0   0   1   1   x1   x1^2 - 2*x1 + 1   -x1 + 1    x1 - 1        x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^8 + 11*x1^7 - 47*x1^6 + 102*x1^5 - 123*x1^4 + 83*x1^3 - 29*x1^2 + 4*x1)
avoiding the zero loci of the polynomials
RingElem[x1 - 2, x1 - 1, x1^2 - 3*x1 + 1, x1 - 3, x1^3 - 4*x1^2 + 4*x1 - 2, x1^3 - 4*x1^2 + 3*x1 - 1, x1, x1^2 - x1 - 1, x1^2 - 4*x1 + 2, 2, x1^2 - x1 + 1]