The realization space is
  [1   0   1   1   0   1         1        0                 x1                 x1]
  [0   1   1   0   0   1   -x1 + 1   x1 - 1   -x1^2 + 3*x1 - 1   -x1^2 + 3*x1 - 1]
  [0   0   0   1   1   1        x1      -x1   -x1^2 + 3*x1 - 1               x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-2*x1^7 + 13*x1^6 - 36*x1^5 + 55*x1^4 - 50*x1^3 + 27*x1^2 - 8*x1 + 1)
avoiding the zero loci of the polynomials
RingElem[x1^2 - 3*x1 + 1, 2*x1 - 1, x1 - 1, x1, 2*x1^2 - 4*x1 + 1, 2*x1^3 - 6*x1^2 + 4*x1 - 1, x1 - 2]