Part A: the worked example of Section 6
  ok   the three sets are convex
  ok   I(v) as in Table 1
  ok   the vertices 3, 5, 6, 7, 9 lie in all three sets; three different roots: a three-set instance
  ok   (PC) holds (all paths enumerated)
  ok   (LOC) holds
  ok   the entries of Table 1 are defined exactly for the indices of J(v)
  ok   the listed assignment satisfies (A1)-(A3) at every vertex
  ok   (P) holds at every vertex
       (P) at v = 9: f_1-f_2: -1 > -2 (tail 5); f_1-f_3: -1 > -2 (tail 5); f_2-f_1: 1 > 0 (tail 6); f_2-f_3: 0 > -1 (tail 6); f_3-f_1: 1 > -2 (tail 7); f_3-f_2: 0 > -1 (tail 7)
  ok   F_1, F_2, F_3 are independent (explicit root paths, Definition 2.1)
       root paths to 9: [[0, 5, 9], [1, 4, 6, 9], [2, 3, 7, 9]]
  ok   root paths to 9 are 0,5,9 / 1,4,6,9 / 2,3,7,9
       families of independent arborescences: 6; on the vertices 0..8: 5, of which 2 cannot be extended to 9
  ok   6 families; 5 families on the vertices 0..8; 2 of them cannot be extended to vertex 9
  ok   the listed family is one of the 6
       vertex 3: costs of the admissible assignments: 0
       vertex 4: costs of the admissible assignments: 0
       vertex 5: costs of the admissible assignments: 0
       vertex 6: costs of the admissible assignments: -4, 0, 1, 2
       vertex 7: costs of the admissible assignments: -2, 0, 2, 3
       vertex 8: costs of the admissible assignments: 0
       vertex 9: costs of the admissible assignments: -3, -1, -1, 0, 1, 2
  ok   for the listed potential the listed assignment is the only one of minimum cost at every vertex
Part B: the small instances of the note
  ok   2.3(a): (PC) fails
  ok   2.3(a): with the vertex condition alone, F_1 = F_2 = D is an independent family
  ok   2.3(a): (ARB) fails (Definition 2.1)
  ok   2.3(b): both sets are convex
  ok   2.3(b): weakly independent arborescences exist and the weak path condition holds
  ok   2.3(b): (PC) fails and (ARB) fails
  ok   2.3(b): (LOC) fails, (LOC_w) holds
  ok   Section 4, first instance: U_1 is not convex
  ok   Section 4, first instance: (PC) holds, (ARB) fails, (LOC) fails
  ok   Section 4, second instance: U_1 is not convex, U_2 is convex
  ok   Section 4, second instance: (PC) and (LOC) hold, (ARB) fails
Part C: Remark 3.2 (the local condition as a bipartite matching problem), random local configurations
       configurations tested: 20000, with an admissible assignment: 11172, disagreements: 0
  ok   Remark 3.2: admissible assignment exists <=> matching covering J(v) exists
TOTAL failures: 0
