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