The realization space is
  [1   1   0    1   0   1   1          0      2*x1 - 1        x1 - 1          1]
  [1   0   1   x1   0   1   0   2*x1 - 1   2*x1^2 - x1   2*x1^2 - x1   2*x1 - 1]
  [0   0   0    0   1   1   1     x1 - 1          x1^2     x1^2 - x1         x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-4*x1^7 + 24*x1^6 - 57*x1^5 + 69*x1^4 - 45*x1^3 + 15*x1^2 - 2*x1)
avoiding the zero loci of the polynomials
RingElem[x1, 2*x1 - 1, x1 - 1, 3*x1 - 2, x1^2 + x1 - 1, 2, x1 + 1, 3*x1^2 - 3*x1 + 1, 2*x1^2 - 2*x1 + 1, x1^2 - x1 + 1]