bottleneck-2: pazz bugs

[Numero7]

There are now two versions of the bottleneck-2, both controllable for two tokens, not more.
I have make all previously hidden edges visible for clarity.
The strategy for both should be to play ba# until you have one token each at states "l" and "r", then play "b1"

the example with suffix "free" is meant to allow to pass tokens through the left and right in any order, as the other side ignores its actions;

   Problem: the "staged" one looks great, except that it is not picked up that two tokens upfront should be controllable.

It does show a correct continuation strategy from l:1, r:1 though, but does not advise to play "b" from s:2.
Bug??

   update: the "free" example does terminate but takes longer than I expected.

Still the same issue with this version:

Play action 'b' in the downward-closure of
( _ , _ , _ , _ , _ , _ , _ , 1 , _ , _ , _ ) // the position corresponds to state s and this is the only tuple

Originally posted by @pazz in #45 (comment)

[Numero7]

./target/release/shepherd -s topological -i dot -f examples/bottleneck-2-staged.dot
Answer: uncontrollable
States:
( s , l , r , l1 , l2 , r1 , c1 , r2 , c2 , c , e )

Play action 'a' in the downward-closure of
( _ , 1 , _ , _ , _ , _ , _ , _ , _ , _ , _ )
( _ , _ , 1 , _ , _ , _ , _ , _ , _ , _ , _ )

Play action 'b' in the downward-closure of
( 1 , _ , _ , _ , _ , _ , _ , _ , _ , _ , _ )

Play action 'b1' in the downward-closure of
( _ , 1 , 1 , _ , _ , _ , _ , _ , _ , _ , _ )
( _ , 1 , _ , _ , _ , _ , _ , _ , ω , _ , _ )
( _ , 1 , _ , _ , _ , _ , _ , ω , _ , _ , _ )
( _ , 1 , _ , _ , ω , _ , _ , _ , _ , _ , _ )

Play action 'b2' in the downward-closure of
( _ , _ , _ , _ , _ , _ , _ , _ , _ , ω , _ )

Play action 'c1' in the downward-closure of
( _ , _ , _ , ω , _ , _ , _ , _ , ω , _ , _ )
( _ , _ , _ , ω , _ , _ , _ , ω , _ , _ , _ )
( _ , _ , _ , ω , ω , _ , _ , _ , _ , _ , _ )

Play action 'c2' in the downward-closure of
( _ , _ , _ , _ , ω , _ , _ , _ , _ , ω , _ )

Play action 'd1' in the downward-closure of
( _ , _ , _ , _ , _ , ω , _ , _ , ω , _ , _ )
( _ , _ , _ , _ , _ , ω , _ , ω , _ , _ , _ )
( _ , _ , _ , _ , ω , ω , _ , _ , _ , _ , _ )

Play action 'd2' in the downward-closure of
( _ , _ , _ , _ , _ , _ , _ , ω , _ , ω , _ )

Play action 'e' in the downward-closure of
( _ , _ , _ , _ , _ , _ , _ , _ , _ , ω , _ )

Play action 'e1' in the downward-closure of
( _ , _ , _ , _ , _ , _ , ω , _ , ω , _ , _ )
( _ , _ , _ , _ , _ , _ , ω , ω , _ , _ , _ )
( _ , _ , _ , _ , ω , _ , ω , _ , _ , _ , _ )

Play action 'e2' in the downward-closure of
( _ , _ , _ , _ , _ , _ , _ , _ , ω , ω , _ )

[Numero7]

[Numero7]

minimal bug reproduction

fn test_path_problem() {

running 1 test
semigroup

( _ , 1 , 1 )
( _ , _ , _ )
( _ , _ , _ )

path_problem_solution
( 1 , _ , _ )

[Numero7]

Minimal bug2 repro

running 1 test
semigroup

( _ , 1 , 1 , _ )
( _ , _ , _ , _ )
( _ , _ , _ , _ )
( _ , _ , _ , _ )

( _ , _ , _ , 1 )
( _ , _ , _ , _ )
( _ , _ , _ , _ )
( _ , _ , _ , _ )

( _ , _ , _ , _ )
( _ , _ , _ , 1 )
( _ , _ , _ , 1 )
( _ , _ , _ , _ )

path_problem_solution
( 1 , _ , _ , _ )
( _ , 1 , 1 , _ )
( _ , _ , _ , _ )

[Numero7]

deep bug: handling constants > 1 in the path problem (handled by polynomial blowup of the state space in the paper)