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