
| a     | b   | c(free)   | c(bound)   d (free)   | d (bound)   | e(free)   | e ( bo und )   |
|-------|-----|-----------|-----------------------|-------------|-----------|----------------|
| cost  |     |           |                       |             |           |                |
| nsols | .1  |           |                       |             |           |                |
| cn    | .1  | 9         |                       |             |           |                |

contains cost values of  (  ) when  (  ) or  (  ) have alread  bound   .   ore ample, cc of o as follows. (The names of the nodes are as in   igure   .)

1. The root of the divisibilit tree, 1, has empt binding set ( 1)    , and the associated subgoal set ( 1 )
tioned into two subsets under ( 1) one independent
(  )  (  )  (  ) .  These two subsets correspond to two child  nodes of the   N
node 1 . . and . . both with empt binding sets.
(  ) is independent under  (  ). Therefore,    is a leaf, and its sole candidate ordering is obtained b  sorting its subgoals b under ( ). . ( )
( )
thus

( ) is indivisible under ( ). Therefore, is an    node, and its three children are created one for each subgoal of ( ) serving as the binder.
inder ( ) ields the child node with the associated set ( )       ( )       ( )
and the binding set (  )      (  ) .   (   ) is independent under   (   ). There fore, is a leaf, and its sole candidate is obtained b  sorting its subgoals b

$${\bigl(}{\quad\quad}{\bigl(}{\quad\quad}{\bigr)}{\bigr)}_{\in{\bigl(}X{\bigr)}}{\qquad\qquad{\bigl(}{\quad\quad}{\bigl(}{\quad\quad}{\bigr)}{\bigr)}_{\in{\bigl(}X{\bigr)}}$$
$$\left(\begin{array}{c}{{}}\\ {{}}\end{array}\right)\ .$$
$\small0$ . 
thus, the candidate of     is    (   ).  (    ).

inder  (  )  ields the child node    with the associated set   (   )
( ) ( )
and the binding set ( ) and ( ) . ( ) is independent under ( ), and its sorting b inder ( ) ields the child node with the associated set ( )
and the binding set ( ) and ( ) is independent under ( ), and its produces the candidate  (  ). (  ).

sorting b e now add each binder to its corresponding child s candidate and obtain three order

ings of the       node         (   )    (   ),   (   )   (   ),   (   )  (   )  (   )  (   ).
e now perform folding of these orderings and check violations of the ad acenc restriction, in order to determine whether a block has a cheaper permutation.