Solved with three auxiliary generators

3 unique, 3 total

Σ#PresentationProperties
Solved by morph:3/0,6/0,7/0:
1111071⟨a, b | baab=aaa, bbbb=1⟩Noc Inf
Solved by morph:4/0,4/0,5/0:
1115365⟨a, b | aba=bb, aaaaaa=1⟩Noc Inf
Solved by custom:0:
1117655⟨a, b | aaaa=1, ababb=ba⟩Noc Inf