Certificate for #19532 ⟨a, b | aab=b, aabbb=aa⟩

Back:⟨a, b | aab=b, aabbb=aa⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #1.

Referenced by [2], [3], [4].

[2] bbb=aa

Axiom: aabbb=aa.

Reduce LHS:

[1](aab)bb
⇒ bbb

Defines rule #3.

Referenced by [3], [4].

[3] aaaa=aa

Overlap of [1] aab=b with [2] bbb=aa:

aa b bbb

Critical pair: aaaa=bbb.

Reduce RHS:

[2](bbb)
⇒ aa

Defines rule #4.

[4] baa=b

Overlap of [2] bbb=aa with [2] bbb=aa:

b bb bbb

Critical pair: baa=aab.

Reduce RHS:

[1](aab)
⇒ b

Defines rule #2.