arcs: [(0, 3), (0, 4), (0, 5), (1, 3), (1, 4), (2, 3), (2, 5), (3, 6), (3, 7), (4, 5), (4, 6), (4, 7), (5, 6), (5, 9), (6, 7), (6, 8), (6, 9), (7, 9)]
convex: [True, True, True]
I(v): {3: [1, 2, 3], 4: [1, 2], 5: [1, 2, 3], 6: [1, 2, 3], 7: [1, 2, 3], 8: [2], 9: [1, 2, 3]}
(PC): True  (LOC): True  three pairwise different roots at one vertex: True
number of families of independent arborescences (claim: 6): 6
number of families on vertices 0..8 (claim: 5): 5
families on 0..8 found by full enumeration: 5
extensions of each of them to vertex 9: [2, 0, 0, 2, 2]  -> not extendable: 2 (claim: 2);  total families: 6
  vertex 3: admissible assignments 1, costs ['0'], listed one has cost 0, unique minimum: True
  vertex 4: admissible assignments 1, costs ['0'], listed one has cost 0, unique minimum: True
  vertex 5: admissible assignments 1, costs ['0'], listed one has cost 0, unique minimum: True
  vertex 6: admissible assignments 4, costs ['-4', '0', '1', '2'], listed one has cost -4, unique minimum: True
  vertex 7: admissible assignments 4, costs ['-2', '0', '2', '3'], listed one has cost -2, unique minimum: True
  vertex 8: admissible assignments 1, costs ['0'], listed one has cost 0, unique minimum: True
  vertex 9: admissible assignments 6, costs ['-3', '-1', '-1', '0', '1', '2'], listed one has cost -3, unique minimum: True
(A1)-(A3): the listed assignment is admissible at every vertex; it is the unique one of minimum cost
(P) holds: True
independent (explicit paths): True
root paths to 9: [[0, 5, 9], [1, 4, 6, 9], [2, 3, 7, 9]]  (claim: 0,5,9; 1,4,6,9; 2,3,7,9)
root paths to 7: [[0, 5, 6, 7], [1, 4, 7], [2, 3, 7]]  (claim: 0,5,6,7; 1,4,7; 2,3,7)
check_example: all statements of Section 4 reproduced
