The realization space is
  [1   1   0           x1^2 - x1   0   1   1          0           x1^2 - x1     x1 - 1                   x1]
  [0   1   1   2*x1^2 - 4*x1 + 1   0   0   1   2*x1 - 1   2*x1^2 - 4*x1 + 1   2*x1 - 1   -2*x1^2 + 4*x1 - 1]
  [0   0   0                   0   1   1   1        -x1               -x1^2        -x1                 x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-4*x1^7 + 10*x1^6 - 6*x1^5 + x1^4)
avoiding the zero loci of the polynomials
RingElem[x1, 3*x1 - 1, x1^2 - 3*x1 + 1, 2*x1 - 1, 2*x1^3 - 4*x1^2 + 4*x1 - 1, x1 - 1, 2*x1^2 - 4*x1 + 1, x1^3 - 6*x1^2 + 5*x1 - 1, x1^2 + 2*x1 - 1, 2]