The realization space is
  [1   1   0   x1 + 1   0   1     1   1        0      x1 + 1]
  [0   1   1     2*x1   0   0     0   1        2        2*x1]
  [0   0   0        0   1   1   -x1   1   x1 + 1   x1^2 + x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (2*x1^7 + 6*x1^6 - 12*x1^4 - 6*x1^3 + 6*x1^2 + 4*x1)
avoiding the zero loci of the polynomials
RingElem[x1, 2, x1 - 1, x1 + 1, x1^2 + 2*x1 - 1, x1 + 3]