The realization space is
  [1   0   1    x1^2 - 2*x1 + 1   0   1    0    1    x1^2 - 2*x1 + 1   x1 - 1   x1 - 1]
  [0   1   1   -2*x1^2 - x1 + 1   0   0    1    1   -2*x1^2 - x1 + 1    -2*x1    -2*x1]
  [0   0   0                  0   1   1   -1   x1          x1^2 + x1   x1 - 1     2*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (4*x1^10 - 4*x1^9 - 17*x1^8 + 5*x1^7 + 18*x1^6 - 2*x1^5 - 5*x1^4 + x1^3)
avoiding the zero loci of the polynomials
RingElem[2, x1, x1 + 1, 3*x1 - 1, x1 - 3, 2*x1^2 - x1 + 1, 2*x1 - 1, 4*x1^3 - x1^2 + 2*x1 - 1, x1 - 1]