The realization space is
  [1   1   0               1   0   1   1           0               1              1              1]
  [1   0   1   x1^2 - x1 - 1   0   1   0           1   x1^2 - x1 - 1   -x1^2 + 2*x1   -x1^2 + 2*x1]
  [0   0   0               0   1   1   1   x1^2 - x1              x1   -x1^2 + 2*x1             x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal with 2 generators
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1 - 2, x1^2 - x1 - 1, x1^2 - 3*x1 + 3, x1^4 - 2*x1^3 + x1 + 1, x1^3 - 2*x1^2 + x1 + 1, x1^2 - 3*x1 + 1, x1^3 - 2*x1^2 + x1 - 1, x1^4 - 4*x1^3 + 4*x1^2 - x1 + 1, x1^3 - x1^2 - x1 - 1, x1^4 - 2*x1^3 + 2, x1^3 - 2*x1^2 - x1 + 1, 2*x1^2 - 4*x1 + 1, x1^4 - 4*x1^3 + 6*x1^2 - 3*x1 - 1, x1^2 - x1 + 1, x1^4 - 3*x1^3 + 3*x1^2 - x1 - 1, x1^4 - 2*x1^3 + x1^2 - x1 - 1, x1^5 - 3*x1^4 + 3*x1^3 - x1^2 + 1, x1^5 - 3*x1^4 + 3*x1^3 - 2*x1^2 + x1 + 1]