Solved with two auxiliary generators

Up:Monoid enumeration
10 unique, 11 total

Σ#PresentationPropertiesφ
Solved by morph:2/0,2/0:
1122833⟨a, b | aaa=1, baabb=abb⟩Noc Inf
Solved by morph:2/0,4/0:
1114591⟨a, b | aaba=a, bbabb=a⟩Noc Inf
Solved by morph:2/0,12/0:
1122860⟨a, b | aaa=1, bbbbb=aba⟩Noc Inf
Solved by morph:3/0,7/0:
1121749⟨a, b | aaa=1, abbbbba=b⟩Noc Inf
Solved by morph:3/0,10/0:
104107⟨a, b | bab=aaa, bbbb=1⟩Noc Inf1
Solved by morph:3/0,13/0:
1110660⟨a, b | aaaa=bab, bbbb=1⟩Noc Inf
Solved by morph:4/0,4/0:
1117137⟨a, b | aaaa=1, abbbba=b⟩Noc Inf
Solved by morph:5/0,5/0:
1121739⟨a, b | aaa=1, abbabba=b⟩Noc Inf
Solved by morph:6/0,7/0:
1117663⟨a, b | aaaa=1, abbba=bb⟩Noc Inf
Solved by morph:3/1,7/0:
1114293⟨a, b | abba=b, aaaaaa=1⟩Noc Inf