The realization space is
  [1   0   1   x1 - 1   0   1    0        1      x1 - 1   x1 - 1      x1 - 1]
  [0   1   1     x1^2   0   0    1        1        x1^2       x1          x1]
  [0   0   0        0   1   1   -1   x1 - 1   x1^2 - x1   x1 - 1   x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^10 - 9*x1^9 + 34*x1^8 - 72*x1^7 + 95*x1^6 - 81*x1^5 + 44*x1^4 - 14*x1^3 + 2*x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x1^2 - x1 + 1, 2*x1 - 1, x1 - 2, x1^3 - 3*x1^2 + 2*x1 - 1, x1^2 - 3*x1 + 1, 2*x1^2 - 2*x1 + 1, x1^3 - 2*x1^2 + x1 - 1]