code: def test_benchmark_coloring():
      V = range(1, 12 + 1)
      E = [
          (1, 2),
          (2, 3),
          (1, 4),
          (1, 6),
          (1, 12),
          (2, 5),
          (2, 7),
          (3, 8),
          (3, 10),
          (4, 11),
          (4, 9),
          (5, 6),
          (6, 7),
          (7, 8),
          (8, 9),
          (9, 10),
          (10, 11),
          (11, 12),
          (5, 12),
          (5, 9),
          (6, 10),
          (7, 11),
          (8, 12),
          (3, 4),
      ]
  
      R, V = xring(["x%d" % v for v in V], QQ, lex)
      E = [(V[i - 1], V[j - 1]) for i, j in E]
  
      x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12 = V
  
      I3 = [x**3 - 1 for x in V]
      Ig = [x**2 + x * y + y**2 for x, y in E]
  
      I = I3 + Ig
  
      assert groebner(I[:-1], R) == [
          x1 + x11 + x12,
          x2 - x11,
          x3 - x12,
          x4 - x12,
          x5 + x11 + x12,
          x6 - x11,
          x7 - x12,
          x8 + x11 + x12,
          x9 - x11,
          x10 + x11 + x12,
          x11**2 + x11 * x12 + x12**2,
          x12**3 - 1,
      ]
  
      assert groebner(I, R) == [1]
  
imports: from sympy.polys.groebnertools import groebner, sig, sig_key, lbp, lbp_key, critical_pair, cp_key, is_rewritable_or_comparable, Sign, Polyn, Num, s_poly, f5_reduce, groebner_lcm, groebner_gcd, is_groebner, is_reduced
  from sympy.polys.fglmtools import _representing_matrices
  from sympy.polys.orderings import lex, grlex
  from sympy.polys.rings import ring, xring
  from sympy.polys.domains import ZZ, QQ
  from sympy.testing.pytest import slow
  from sympy.polys import polyconfig
label_desc: Use image node_id 7 for calling a global function with example usage: test_benchmark_coloring() without return types