The realization space is
  [1   0   1    1   1   0         1   1         1          0    1]
  [0   1   1   x1   0   0         0   1   -x1 + 1          1   x1]
  [0   0   0    0   1   1   -x1 + 1   1        x1   3*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, -2*x1^3 + 5*x1^2 - 4*x1 + 1)
avoiding the zero loci of the polynomials
RingElem[3*x1^2 - 1, x1, 3, 3*x1^2 - 3*x1 - 1, 3*x1^3 - x1 + 1, x1 - 1, 2*x1 - 1, 3*x1 - 1, 3*x1 - 2, 3*x1^2 - 5*x1 + 1, 3*x1^2 - 2*x1 + 1, 3*x1^2 + 1, 6*x1^2 - 3*x1 + 1, 3*x1^3 + x1 - 1, 3*x1^3 - 3*x1^2 + 1, 2, 3*x1^2 - 3*x1 + 2, 3*x1^3 + 1, x1^2 - 3*x1 + 1, 3*x1^3 - 2*x1^2 + 2*x1 - 1, 3*x1^2 - 5*x1 + 3]