Solved with four auxiliary generators

7 unique, 7 total

Σ	#	Presentation	Properties
Solved by `morph:2/0,2/1,3/0,4/0`:
11	5298	⟨a, b \| abaaaba=aaab⟩	Noc Inf
Solved by `morph:2/0,3/1,3/1,5/1`:
11	4342	⟨a, b \| abbabaaab=ba⟩	Can Inf
Solved by `morph:2/1,2/1,2/1,2/0`:
9	1137	⟨a, b \| abbbba=bab⟩	Can Inf
11	5246	⟨a, b \| aabbbaa=baab⟩	Can Inf
Solved by `morph:2/1,2/1,2/1,6/0`:
11	3812	⟨a, b \| abbabaaaab=a⟩	Noc Inf
Solved by `morph:3/2,2/1,3/2,3/0`:
10	2461	⟨a, b \| aaabba=baaa⟩	Noc Inf
Solved by `custom:0`:
11	5109	⟨a, b \| aaabbba=baaa⟩	Noc Inf