EXTERNAL LOOP:
~~~~~~~~~~~~~

IF --besttree, --bestsimple or --bestgreedy specified
	THEN
	let N be the best network obtained by the relevant subroutine
	ELSE
	let N be the result of running the MAIN ALGORITHM.
	ENDIF

- Compute stats for N, display some pre post-processing results

- Mild post-processing on N, unless all post-processing switched off. (This involves
	repeatedly contracting edges with neither endpoint a reticulation, where this does not damage 
	triplet consistency)

- Radical post-processing of N, but ONLY if radical post-processing switched on (and
	post-processing has not been totally disabled). This involves executing the
	following loop:
	
	SD-min loop:
	Keep deleting edges until that doesn't reduce SD anymore
	Keep contracting edges until that doesn't reduce SD anymore
	Go back to Loop for as long as something is deleted or contracted

- List surplus/missing triplets if the user has requested this information

- Display final network (DOT/eNewick)

- Print final stats

FINISHED

-----------------------------------------------------------------------------------------------

The MAIN ALGORITHM consists of running the following MAIN LOOP until we are finished. The high-level
description of the MAIN LOOP is: { try Aho, if that fails try the polytime J&S algorithm, if that
fails then use the J&S "5/12" scoring function. Compute a good simple level-1 network for the triplets
induced by the partition, and (if possible) a good tree, if the tree is better use the tree, otherwise
use the simple level-1 network }.


MAIN LOOP:

1) CHOOSE THE PARTITION
-----------------------

- IF --forcemaxsn is TRUE, use the max SN-sets as a partition, DONE;
ELSE
	IF Aho graph is not connected THEN return a 2-block partition
		where one of the blocks is equal to one of the connected
		components in the Aho graph, and the other is equal to
		the remaining leaves, DONE

	ELSE
			IF we are allowed to look for local perfection (i.e. --noperfection is false) THEN
				look at the max SN-sets of the set: if they
				form a genuine partition of the leaves
				-and- the induced set of triplets is dense
				-and- they are 100% consistent with some
				level-1 network -then- we found local perfection: use
				the max SN-sets as the partition! DONE
		
			ELSE
				Use the J&S "5/12" scoring function to choose
				a partition (up to the maximum number of
				blocks allowed), DONE


2) DECIDE WHAT TO DO WITH THE PARTITION
---------------------------------------

- IF the partition contains only two blocks, then we're done because we introduce a
  tree vertex (i.e. indegree 1, outdegree 2) and we recurse inside the blocks
  ELSE
		- Induce a set of triplets on the partition

		- IF we were allowed to look for local perfection and we found it 
		 		THEN
				introduce a simple level-1 network (constructed using the J&S algorithm) consistent with 100% of the induced triplets, and recurse inside the blocks, done
				ELSE
				
				- IF the number of leaves in the induced triplet set is not
				above the --simmax thresshold
					THEN
					use the exponential-time best simple level-1 algorithm
					ELSE
					use the greedy simple level-1 algorithm

				- IF the number of leaves in the induced triplet set is not above
				the --wumax threshhold,
					THEN
					use Wu's exponential-time algorithm to get the best
					

				Introduce the computed simple level-1 network UNLESS we also ran
				Wu's algorithm and it was better than the computed simple level-1
				algorithm. Recurse inside the blocks, DONE.