The realization space is
  [1   1   0   2*x1^2 - 3*x1 + 1   0   1   1          0   2*x1^2 - 3*x1 + 1   x1 - 1      2*x1 - 1]
  [1   0   1               -x1^2   0   1   0     x1 - 1               -x1^2      -x1          x1^2]
  [0   0   0                   0   1   1   1   2*x1 - 1        -2*x1^2 + x1      -x1   2*x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-16*x1^7 + 40*x1^6 - 44*x1^5 + 26*x1^4 - 8*x1^3 + x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, 3*x1 - 2, x1 - 1, x1^2 + x1 - 1, 2*x1 - 1, 3*x1^2 - 3*x1 + 1, 3*x1 - 1, 2*x1^2 - 2*x1 + 1, x1^2 - 3*x1 + 1, 5*x1^2 - 4*x1 + 1]