Certificate for #13140 ⟨a, b | aab=aaa, bbb=aa⟩

Back:⟨a, b | aab=aaa, bbb=aa⟩

Completion settings:

[1] aab=aaa

Axiom: aab=aaa.

Defines rule #1.

Referenced by [3], [4].

[2] bbb=aa

Axiom: bbb=aa.

Defines rule #3.

Referenced by [3], [4].

[3] baa=aaa

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

b bb bbb

Critical pair: baa=aab.

Reduce RHS:

[1](aab)
⇒ aaa

Defines rule #2.

[4] aaaaa=aaaa

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

aa b bbb

Critical pair: aaaa=aaabb.

Reduce RHS:

[1]a(aab)b
[1]⇒ aa(aab)
⇒ aaaaa

Flip LHS and RHS.

Defines rule #4.