The realization space is
  [1   0   1   0                x2   0                x2                x2    1    1]
  [0   1   1   1   -x1 + x2^2 + x2   0   -x1 + x2^2 + x2                x2    0   x1]
  [0   0   0   1   -x1 + x2^2 + x2   1        -x1 + x2^2   -x1 + x2^2 + x2   x2   x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal with 2 generators
avoiding the zero loci of the polynomials
RingElem[x2, x1, x1 - x2, x1^2 - x1*x2^2 - x1*x2 + x2^2, x1 - 1, x1 - x2^2 - x2, x2 - 1, x1 - x2^2, x1^2 - 2*x1*x2^2 - x1*x2 + x2^3 + x2^2, x1 - x2 - 1, x2 + 1, x1 - x2^2 - x2 - 1, x1*x2 + x1 - x2^3 - x2^2 - x2, x1^2 - 2*x1*x2^2 - x1*x2 + x2^4 + x2^3 + x2^2]