Certificate for #20144 ⟨a, b | aab=b, bbaa=aaa⟩

Back:⟨a, b | aab=b, bbaa=aaa⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Referenced by [3], [4].

[2] aaa=bbaa

Axiom: bbaa=aaa.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3].

[3] ab=bbb

Overlap of [2] aaa=bbaa with [1] aab=b:

a aa aab

Critical pair: ab=bbaab.

Reduce RHS:

[1]bb(aab)
⇒ bbb

Defines rule #2.

Referenced by [4].

[4] bbbbb=b

Overlap of [1] aab=b with [3] ab=bbb:

a ab ab

Critical pair: abbb=b.

Reduce LHS:

[3](ab)bb
⇒ bbbbb

Defines rule #1.