A plays B, C plays D, winners play.  say A beats C by symmetry.
C plays E
IF C WINS, C plays F
  IF C WINS, A plays C twice
    IF A WINS TWICE, A wins the tournament
    IF A AND C SPLIT, A plays C best-of-3
    IF C WINS TWICE, A plays B and winner plays C twice (C wins ties)
  IF F WINS, A plays F twice
    IF A WINS TWICE, C plays D and winner plays A twice (A wins ties)
    IF A AND F SPLIT, A plays F best-of-3
    IF F WINS TWICE, A plays C and winner plays F twice (F wins ties)
IF E WINS, A plays E
  IF A WINS, E plays F
    IF E WINS, A plays E
      IF A WINS, D plays A 3 times and needs to win them all
      IF E WINS, A plays E best-of-3
    IF F WINS, A plays F
      IF A WINS, D plays F and winner plays A twice (A wins ties)
      IF F WINS, A plays F best-of-3
  IF E WINS, A plays E again
    IF A WINS, E plays F
      IF E WINS, A plays E best-of-3
      IF F WINS, A plays F
        IF A WINS, E plays A twice (A wins ties)
        IF F WINS, A plays F twice (F wins ties)
    IF E WINS, E plays F
      IF E WINS, D plays E 3 times and needs to win them all
      IF F WINS, D plays E best-of-3