Certificate for #6710 ⟨a, b | aab=b, bbaa=aa⟩

Back:⟨a, b | aab=b, bbaa=aa⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #1.

Referenced by [3], [4], [5].

[2] bbaa=aa

Axiom: bbaa=aa.

Defines rule #4.

Referenced by [3], [4], [5].

[3] aaaa=aa

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

aa b bbaa

Critical pair: aaaa=bbaa.

Reduce RHS:

[2](bbaa)
⇒ aa

Defines rule #3.

[4] bbb=b

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

bb aa aab

Critical pair: bbb=aab.

Reduce RHS:

[1](aab)
⇒ b

Defines rule #2.

[5] bbab=ab

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

bba a aab

Critical pair: bbab=aaab.

Reduce RHS:

[1]a(aab)
⇒ ab

Defines rule #5.