1000 successive deterministic queue states

//each row is a queue state. queue length is 4, rejection rate is 9/10, # of distinct encounters is 5.
//generated with this script with initial condition corresponding to 00000100. https://pastebin.com/Qmma3TfT
0	0	0	2
0	0	2	1
0	2	1	4
2	1	4	4
1	4	4	3
4	4	3	0
4	3	0	1
3	0	1	2
0	1	2	4
1	2	4	3
2	4	3	4
4	3	4	2
3	4	2	1
4	2	1	0
2	1	0	3
1	0	3	4
0	3	4	2
3	4	2	1
4	2	1	0
2	1	0	4
1	0	4	3
0	4	3	2
4	3	2	4
3	2	4	2
2	4	2	4
4	2	4	2
2	4	2	4
4	2	4	0
2	4	0	1
4	0	1	2
0	1	2	3
1	2	3	4
2	3	4	0
3	4	0	1
4	0	1	0
0	1	0	3
1	0	3	2
0	3	2	0
3	2	0	4
2	0	4	4
0	4	4	3
4	4	3	1
4	3	1	0
3	1	0	2
1	0	2	4
0	2	4	3
2	4	3	1
4	3	1	0
3	1	0	2
1	0	2	2
0	2	2	0
2	2	0	1
2	0	1	4
0	1	4	3
1	4	3	2
4	3	2	0
3	2	0	1
2	0	1	4
0	1	4	3
1	4	3	2
4	3	2	0
3	2	0	2
2	0	2	4
0	2	4	0
2	4	0	0
4	0	0	3
0	0	3	1
0	3	1	4
3	1	4	4
1	4	4	2
4	4	2	3
4	2	3	2
2	3	2	0
3	2	0	4
2	0	4	1
0	4	1	3
4	1	3	2
1	3	2	0
3	2	0	4
2	0	4	0
0	4	0	4
4	0	4	3
0	4	3	1
4	3	1	4
3	1	4	0
1	4	0	2
4	0	2	3
0	2	3	1
2	3	1	4
3	1	4	0
1	4	0	4
4	0	4	2
0	4	2	3
4	2	3	1
2	3	1	0
3	1	0	4
1	0	4	2
0	4	2	3
4	2	3	1
2	3	1	0
3	1	0	4
1	0	4	2
0	4	2	3
4	2	3	1
2	3	1	0
3	1	0	2
1	0	2	4
0	2	4	3
2	4	3	2
4	3	2	1
3	2	1	0
2	1	0	4
1	0	4	4
0	4	4	2
4	4	2	1
4	2	1	0
2	1	0	0
1	0	0	3
0	0	3	2
0	3	2	1
3	2	1	4
2	1	4	4
1	4	4	0
4	4	0	2
4	0	2	0
0	2	0	3
2	0	3	4
0	3	4	1
3	4	1	2
4	1	2	0
1	2	0	3
2	0	3	2
0	3	2	1
3	2	1	4
2	1	4	0
1	4	0	4
4	0	4	2
0	4	2	1
4	2	1	3
2	1	3	0
1	3	0	4
3	0	4	2
0	4	2	1
4	2	1	2
2	1	2	3
1	2	3	0
2	3	0	4
3	0	4	2
0	4	2	1
4	2	1	0
2	1	0	3
1	0	3	4
0	3	4	0
3	4	0	3
4	0	3	4
0	3	4	3
3	4	3	1
4	3	1	2
3	1	2	0
1	2	0	0
2	0	0	4
0	0	4	0
0	4	0	1
4	0	1	2
0	1	2	2
1	2	2	1
2	2	1	3
2	1	3	0
1	3	0	4
3	0	4	2
0	4	2	1
4	2	1	4
2	1	4	0
1	4	0	3
4	0	3	2
0	3	2	0
3	2	0	4
2	0	4	4
0	4	4	1
4	4	1	2
4	1	2	0
1	2	0	3
2	0	3	4
0	3	4	4
3	4	4	2
4	4	2	1
4	2	1	3
2	1	3	0
1	3	0	0
3	0	0	3
0	0	3	2
0	3	2	4
3	2	4	0
2	4	0	1
4	0	1	2
0	1	2	0
1	2	0	3
2	0	3	4
0	3	4	1
3	4	1	2
4	1	2	0
1	2	0	3
2	0	3	4
0	3	4	4
3	4	4	2
4	4	2	4
4	2	4	0
2	4	0	1
4	0	1	4
0	1	4	2
1	4	2	3
4	2	3	2
2	3	2	0
3	2	0	1
2	0	1	4
0	1	4	4
1	4	4	4
4	4	4	0
4	4	0	0
4	0	0	4
0	0	4	3
0	4	3	2
4	3	2	1
3	2	1	0
2	1	0	0
1	0	0	3
0	0	3	2
0	3	2	1
3	2	1	4
2	1	4	0
1	4	0	3
4	0	3	2
0	3	2	2
3	2	2	1
2	2	1	4
2	1	4	0
1	4	0	3
4	0	3	2
0	3	2	1
3	2	1	4
2	1	4	0
1	4	0	0
4	0	0	4
0	0	4	2
0	4	2	3
4	2	3	1
2	3	1	0
3	1	0	4
1	0	4	2
0	4	2	0
4	2	0	3
2	0	3	1
0	3	1	2
3	1	2	4
1	2	4	0
2	4	0	3
4	0	3	1
0	3	1	0
3	1	0	0
1	0	0	4
0	0	4	2
0	4	2	1
4	2	1	4
2	1	4	0
1	4	0	4
4	0	4	4
0	4	4	2
4	4	2	2
4	2	2	1
2	2	1	3
2	1	3	4
1	3	4	0
3	4	0	2
4	0	2	4
0	2	4	3
2	4	3	1
4	3	1	0
3	1	0	4
1	0	4	4
0	4	4	3
4	4	3	2
4	3	2	0
3	2	0	1
2	0	1	4
0	1	4	2
1	4	2	3
4	2	3	0
2	3	0	1
3	0	1	4
0	1	4	0
1	4	0	2
4	0	2	3
0	2	3	1
2	3	1	4
3	1	4	4
1	4	4	2
4	4	2	0
4	2	0	1
2	0	1	3
0	1	3	4
1	3	4	2
3	4	2	4
4	2	4	0
2	4	0	1
4	0	1	4
0	1	4	4
1	4	4	2
4	4	2	3
4	2	3	0
2	3	0	1
3	0	1	0
0	1	0	2
1	0	2	3
0	2	3	2
2	3	2	4
3	2	4	0
2	4	0	4
4	0	4	1
0	4	1	2
4	1	2	2
1	2	2	3
2	2	3	4
2	3	4	1
3	4	1	4
4	1	4	2
1	4	2	3
4	2	3	0
2	3	0	1
3	0	1	2
0	1	2	0
1	2	0	4
2	0	4	3
0	4	3	1
4	3	1	2
3	1	2	0
1	2	0	0
2	0	0	0
0	0	0	3
0	0	3	2
0	3	2	1
3	2	1	4
2	1	4	0
1	4	0	3
4	0	3	2
0	3	2	1
3	2	1	4
2	1	4	2
1	4	2	0
4	2	0	3
2	0	3	4
0	3	4	1
3	4	1	2
4	1	2	2
1	2	2	0
2	2	0	4
2	0	4	1
0	4	1	3
4	1	3	2
1	3	2	0
3	2	0	4
2	0	4	2
0	4	2	3
4	2	3	0
2	3	0	1
3	0	1	0
0	1	0	4
1	0	4	3
0	4	3	2
4	3	2	0
3	2	0	2
2	0	2	4
0	2	4	3
2	4	3	1
4	3	1	0
3	1	0	2
1	0	2	4
0	2	4	3
2	4	3	1
4	3	1	0
3	1	0	4
1	0	4	4
0	4	4	1
4	4	1	3
4	1	3	2
1	3	2	0
3	2	0	4
2	0	4	1
0	4	1	3
4	1	3	2
1	3	2	0
3	2	0	4
2	0	4	4
0	4	4	3
4	4	3	1
4	3	1	2
3	1	2	0
1	2	0	0
2	0	0	4
0	0	4	1
0	4	1	3
4	1	3	2
1	3	2	4
3	2	4	0
2	4	0	0
4	0	0	3
0	0	3	3
0	3	3	4
3	3	4	1
3	4	1	2
4	1	2	0
1	2	0	2
2	0	2	4
0	2	4	1
2	4	1	3
4	1	3	2
1	3	2	0
3	2	0	4
2	0	4	1
0	4	1	3
4	1	3	0
1	3	0	2
3	0	2	4
0	2	4	1
2	4	1	2
4	1	2	0
1	2	0	3
2	0	3	4
0	3	4	0
3	4	0	3
4	0	3	2
0	3	2	4
3	2	4	4
2	4	4	0
4	4	0	1
4	0	1	2
0	1	2	0
1	2	0	2
2	0	2	3
0	2	3	4
2	3	4	1
3	4	1	0
4	1	0	2
1	0	2	2
0	2	2	3
2	2	3	4
2	3	4	1
3	4	1	0
4	1	0	0
1	0	0	4
0	0	4	3
0	4	3	2
4	3	2	1
3	2	1	0
2	1	0	4
1	0	4	2
0	4	2	4
4	2	4	1
2	4	1	0
4	1	0	4
1	0	4	2
0	4	2	0
4	2	0	3
2	0	3	0
0	3	0	2
3	0	2	1
0	2	1	4
2	1	4	3
1	4	3	0
4	3	0	2
3	0	2	2
0	2	2	1
2	2	1	3
2	1	3	4
1	3	4	0
3	4	0	2
4	0	2	1
0	2	1	3
2	1	3	4
1	3	4	2
3	4	2	0
4	2	0	1
2	0	1	3
0	1	3	4
1	3	4	2
3	4	2	2
4	2	2	0
2	2	0	1
2	0	1	1
0	1	1	4
1	1	4	2
1	4	2	0
4	2	0	3
2	0	3	2
0	3	2	4
3	2	4	1
2	4	1	2
4	1	2	0
1	2	0	3
2	0	3	4
0	3	4	4
3	4	4	2
4	4	2	1
4	2	1	3
2	1	3	0
1	3	0	0
3	0	0	4
0	0	4	2
0	4	2	1
4	2	1	4
2	1	4	3
1	4	3	4
4	3	4	2
3	4	2	4
4	2	4	0
2	4	0	1
4	0	1	3
0	1	3	2
1	3	2	2
3	2	2	4
2	2	4	0
2	4	0	1
4	0	1	0
0	1	0	3
1	0	3	3
0	3	3	1
3	3	1	4
3	1	4	2
1	4	2	0
4	2	0	3
2	0	3	1
0	3	1	4
3	1	4	2
1	4	2	4
4	2	4	0
2	4	0	1
4	0	1	3
0	1	3	2
1	3	2	0
3	2	0	4
2	0	4	1
0	4	1	2
4	1	2	3
1	2	3	0
2	3	0	4
3	0	4	1
0	4	1	2
4	1	2	3
1	2	3	4
2	3	4	0
3	4	0	2
4	0	2	1
0	2	1	3
2	1	3	4
1	3	4	2
3	4	2	4
4	2	4	1
2	4	1	3
4	1	3	2
1	3	2	2
3	2	2	4
2	2	4	0
2	4	0	1
4	0	1	4
0	1	4	3
1	4	3	2
4	3	2	0
3	2	0	2
2	0	2	1
0	2	1	3
2	1	3	2
1	3	2	4
3	2	4	0
2	4	0	1
4	0	1	3
0	1	3	0
1	3	0	0
3	0	0	4
0	0	4	1
0	4	1	2
4	1	2	3
1	2	3	4
2	3	4	0
3	4	0	1
4	0	1	4
0	1	4	2
1	4	2	3
4	2	3	0
2	3	0	1
3	0	1	4
0	1	4	2
1	4	2	3
4	2	3	0
2	3	0	1
3	0	1	4
0	1	4	2
1	4	2	3
4	2	3	0
2	3	0	4
3	0	4	1
0	4	1	2
4	1	2	3
1	2	3	0
2	3	0	2
3	0	2	1
0	2	1	4
2	1	4	3
1	4	3	0
4	3	0	2
3	0	2	1
0	2	1	4
2	1	4	3
1	4	3	2
4	3	2	0
3	2	0	1
2	0	1	0
0	1	0	3
1	0	3	2
0	3	2	4
3	2	4	1
2	4	1	0
4	1	0	3
1	0	3	0
0	3	0	2
3	0	2	4
0	2	4	1
2	4	1	3
4	1	3	0
1	3	0	2
3	0	2	4
0	2	4	1
2	4	1	3
4	1	3	0
1	3	0	4
3	0	4	2
0	4	2	4
4	2	4	1
2	4	1	3
4	1	3	0
1	3	0	2
3	0	2	4
0	2	4	1
2	4	1	3
4	1	3	0
1	3	0	2
3	0	2	4
0	2	4	4
2	4	4	3
4	4	3	0
4	3	0	2
3	0	2	1
0	2	1	4
2	1	4	0
1	4	0	3
4	0	3	2
0	3	2	1
3	2	1	4
2	1	4	0
1	4	0	3
4	0	3	2
0	3	2	4
3	2	4	1
2	4	1	2
4	1	2	3
1	2	3	2
2	3	2	4
3	2	4	0
2	4	0	1
4	0	1	3
0	1	3	2
1	3	2	2
3	2	2	0
2	2	0	1
2	0	1	3
0	1	3	4
1	3	4	0
3	4	0	2
4	0	2	2
0	2	2	3
2	2	3	1
2	3	1	0
3	1	0	2
1	0	2	4
0	2	4	2
2	4	2	1
4	2	1	0
2	1	0	3
1	0	3	4
0	3	4	2
3	4	2	1
4	2	1	0
2	1	0	4
1	0	4	3
0	4	3	2
4	3	2	1
3	2	1	2
2	1	2	4
1	2	4	0
2	4	0	0
4	0	0	3
0	0	3	1
0	3	1	2
3	1	2	4
1	2	4	4
2	4	4	3
4	4	3	1
4	3	1	0
3	1	0	0
1	0	0	4
0	0	4	2
0	4	2	3
4	2	3	1
2	3	1	0
3	1	0	0
1	0	0	3
0	0	3	4
0	3	4	2
3	4	2	1
4	2	1	0
2	1	0	3
1	0	3	2
0	3	2	0
3	2	0	4
2	0	4	1
0	4	1	0
4	1	0	2
1	0	2	3
0	2	3	4
2	3	4	0
3	4	0	1
4	0	1	0
0	1	0	2
1	0	2	4
0	2	4	3
2	4	3	1
4	3	1	0
3	1	0	2
1	0	2	4
0	2	4	3
2	4	3	0
4	3	0	1
3	0	1	2
0	1	2	4
1	2	4	3
2	4	3	0
4	3	0	4
3	0	4	1
0	4	1	2
4	1	2	4
1	2	4	0
2	4	0	2
4	0	2	1
0	2	1	3
2	1	3	4
1	3	4	0
3	4	0	4
4	0	4	2
0	4	2	1
4	2	1	3
2	1	3	2
1	3	2	4
3	2	4	0
2	4	0	0
4	0	0	3
0	0	3	2
0	3	2	1
3	2	1	0
2	1	0	4
1	0	4	0
0	4	0	3
4	0	3	1
0	3	1	2
3	1	2	4
1	2	4	0
2	4	0	3
4	0	3	4
0	3	4	2
3	4	2	4
4	2	4	1
2	4	1	3
4	1	3	2
1	3	2	0
3	2	0	4
2	0	4	2
0	4	2	1
4	2	1	0
2	1	0	3
1	0	3	2
0	3	2	4
3	2	4	2
2	4	2	0
4	2	0	1
2	0	1	3
0	1	3	4
1	3	4	2
3	4	2	0
4	2	0	1
2	0	1	4
0	1	4	3
1	4	3	2
4	3	2	0
3	2	0	2
2	0	2	4
0	2	4	1
2	4	1	3
4	1	3	0
1	3	0	4
3	0	4	2
0	4	2	1
4	2	1	3
2	1	3	0
1	3	0	4
3	0	4	2
0	4	2	1
4	2	1	0
2	1	0	3
1	0	3	0
0	3	0	2
3	0	2	4
0	2	4	2
2	4	2	1
4	2	1	0
2	1	0	3
1	0	3	4
0	3	4	2
3	4	2	1
4	2	1	2
2	1	2	1
1	2	1	3
2	1	3	0
1	3	0	4
3	0	4	4
0	4	4	1
4	4	1	3
4	1	3	0
1	3	0	2
3	0	2	4
0	2	4	1
2	4	1	3
4	1	3	0
1	3	0	2
3	0	2	4
0	2	4	4
2	4	4	3
4	4	3	1
4	3	1	0
3	1	0	0
1	0	0	4
0	0	4	2
0	4	2	4
4	2	4	3
2	4	3	4
4	3	4	1
3	4	1	3
4	1	3	2
1	3	2	4
3	2	4	0
2	4	0	1
4	0	1	0
0	1	0	3
1	0	3	2
0	3	2	4
3	2	4	1
2	4	1	0
4	1	0	3
1	0	3	2
0	3	2	0
3	2	0	4
2	0	4	4
0	4	4	3
4	4	3	1
4	3	1	0
3	1	0	2
1	0	2	4
0	2	4	3
2	4	3	1
4	3	1	0
3	1	0	4
1	0	4	2
0	4	2	4
4	2	4	3
2	4	3	1
4	3	1	0
3	1	0	0
1	0	0	3
0	0	3	2
0	3	2	4
3	2	4	4
2	4	4	0
4	4	0	3
4	0	3	2
0	3	2	1
3	2	1	2
2	1	2	0
1	2	0	3
2	0	3	4
0	3	4	1
3	4	1	2
4	1	2	0
1	2	0	4
2	0	4	3
0	4	3	4
4	3	4	1
3	4	1	0
4	1	0	2
1	0	2	3
0	2	3	0
2	3	0	1
3	0	1	4
0	1	4	4
1	4	4	3
4	4	3	2
4	3	2	1
3	2	1	0
2	1	0	4
1	0	4	3
0	4	3	0
4	3	0	1
3	0	1	2
0	1	2	0
1	2	0	3
2	0	3	0
0	3	0	3
3	0	3	2
0	3	2	4
3	2	4	1
2	4	1	0
4	1	0	3
1	0	3	4
0	3	4	2
3	4	2	1
4	2	1	4
2	1	4	4
1	4	4	0
4	4	0	2
4	0	2	1
0	2	1	3
2	1	3	4
1	3	4	0
3	4	0	0
4	0	0	2
0	0	2	2
0	2	2	1
2	2	1	4
2	1	4	0
1	4	0	0
4	0	0	2
0	0	2	3
0	2	3	4
2	3	4	2
3	4	2	1
4	2	1	4
2	1	4	3
1	4	3	0
4	3	0	2
3	0	2	2
0	2	2	1
2	2	1	3
2	1	3	0
1	3	0	4
3	0	4	2
0	4	2	1
4	2	1	3
2	1	3	0
1	3	0	2
3	0	2	0
0	2	0	2
2	0	2	4
0	2	4	1
2	4	1	3
4	1	3	2
1	3	2	0
3	2	0	2
2	0	2	1
0	2	1	4
2	1	4	3
1	4	3	0
4	3	0	2
3	0	2	1
0	2	1	4
2	1	4	3
1	4	3	0
4	3	0	0
3	0	0	1
0	0	1	2
0	1	2	4
1	2	4	3
2	4	3	4
4	3	4	1
3	4	1	3
4	1	3	2
1	3	2	4
3	2	4	0
2	4	0	1
4	0	1	3
0	1	3	2
1	3	2	4
3	2	4	2
2	4	2	1
4	2	1	0
2	1	0	2