Certificate for #16524 ⟨a, b | aab=bb, bbb=aaa⟩

Back:⟨a, b | aab=bb, bbb=aaa⟩

Completion settings:

[1] aab=bb

Axiom: aab=bb.

Defines rule #4.

Referenced by [3], [5].

[2] aaa=bbb

Axiom: bbb=aaa.

Flip LHS and RHS.

Defines rule #5.

Referenced by [3], [4].

[3] abb=bbbb

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

a aa aab

Critical pair: abb=bbbb.

Defines rule #2.

Referenced by [4], [5].

[4] bbba=bbbbb

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

a aa aaa

Critical pair: abbb=bbba.

Reduce LHS:

[3](abb)b
⇒ bbbbb

Flip LHS and RHS.

Defines rule #3.

[5] bbbbbb=bbb

Overlap of [1] aab=bb with [3] abb=bbbb:

a ab abb

Critical pair: abbbb=bbb.

Reduce LHS:

[3](abb)bb
⇒ bbbbbb

Defines rule #1.