timestamps
  vertex :     s     t     u     v     w     x     y     z
  d/f    : 1/10 11/16 14/15 12/13 7/8   4/5   3/6   2/9  

parenthesization
  (s (z (y (x x) y) (w w) z) s) (t (v v) (u u) t) 

edge classification
  s->z  tree
  z->y  tree
  y->x  tree
  x->z  back
  z->w  tree
  w->x  cross
  s->w  forward
  t->v  tree
  v->w  cross
  v->s  cross
  t->u  tree
  u->t  back
  u->v  cross
