Certificate for #5308 ⟨a, b | aaa=aa, bbb=aa⟩

Back:⟨a, b | aaa=aa, bbb=aa⟩

Completion settings:

[1] aaa=aa

Axiom: aaa=aa.

Referenced by [3].

[2] aa=bbb

Axiom: bbb=aa.

Flip LHS and RHS.

Defines rule #4.

Referenced by [3], [4], [5], [6].

[3] aaa=bbb

Simplify [1] aaa=aa.

Reduce RHS:

[2](aa)
⇒ bbb

Referenced by [4].

[4] bbba=bbb

Overlap of [3] aaa=bbb with [2] aa=bbb:

aaa aa

Critical pair: bbba=bbb.

Defines rule #3.

Referenced by [5].

[5] abbb=bbb

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

a a aa

Critical pair: abbb=bbba.

Reduce RHS:

[4](bbba)
⇒ bbb

Defines rule #2.

Referenced by [6].

[6] bbbbbb=bbb

Overlap of [2] aa=bbb with [5] abbb=bbb:

a a abbb

Critical pair: abbb=bbbbbb.

Reduce LHS:

[5](abbb)
⇒ bbb

Flip LHS and RHS.

Defines rule #1.