The realization space is
  [1   1   0           4*x1^2 - 4*x1 + 1   0   1   1                  0           4*x1^2 - 4*x1 + 1           2*x1 - 1           2*x1 - 1]
  [0   1   1   -x1^3 + 3*x1^2 - 3*x1 + 1   0   0   1   -x1^2 + 2*x1 - 1   -x1^3 + 3*x1^2 - 3*x1 + 1   -x1^2 + 2*x1 - 1   -x1^2 + 2*x1 - 1]
  [0   0   0                           0   1   1   1        2*x1^2 - x1               2*x1^3 - x1^2               x1^2        2*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, x1 - 1, 2*x1 - 1, 3*x1^2 - 3*x1 + 1, x1^3 + 2*x1^2 - 3*x1 + 1, x1^2 + x1 - 1, x1^4 + 3*x1^3 - 6*x1^2 + 4*x1 - 1, 2*x1^2 - 2*x1 + 1, 3*x1 - 2, 5*x1^3 - 7*x1^2 + 4*x1 - 1, 3*x1^3 - 4*x1^2 + 3*x1 - 1]