Certificate for #19523 ⟨a, b | aab=b, aabaa=bb⟩

Back:⟨a, b | aab=b, aabaa=bb⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #2.

Referenced by [2], [3].

[2] bb=baa

Axiom: aabaa=bb.

Reduce LHS:

[1](aab)aa
⇒ baa

Flip LHS and RHS.

Defines rule #3.

Referenced by [3].

[3] baaaa=baa

Overlap of [2] bb=baa with [2] bb=baa:

b b bb

Critical pair: bbaa=baab.

Reduce LHS:

[2](bb)aa
⇒ baaaa

Reduce RHS:

[1]b(aab)
[2]⇒ (bb)
⇒ baa

Defines rule #1.