Certificate for #13110 ⟨a, b | bbb=aaa, aaaa=a⟩

Back:⟨a, b | bbb=aaa, aaaa=a⟩

Completion settings:

[1] aaa=bbb

Axiom: bbb=aaa.

Flip LHS and RHS.

Defines rule #1.

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

[2] bbba=a

Axiom: aaaa=a.

Reduce LHS:

[1](aaa)a
⇒ bbba

Defines rule #2.

Referenced by [3], [4].

[3] abbb=a

Overlap of [1] aaa=bbb with [1] aaa=bbb:

a aa aaa

Critical pair: abbb=bbba.

Reduce RHS:

[2](bbba)
⇒ a

Defines rule #3.

[4] bbbbbb=bbb

Overlap of [2] bbba=a with [1] aaa=bbb:

bbb a aaa

Critical pair: bbbbbb=aaa.

Reduce RHS:

[1](aaa)
⇒ bbb

Defines rule #4.