Certificate for #13174 ⟨a, b | aba=aab, bbb=aa⟩

Back:⟨a, b | aba=aab, bbb=aa⟩

Completion settings:

[1] aba=aab

Axiom: aba=aab.

Referenced by [3].

[2] aa=bbb

Axiom: bbb=aa.

Flip LHS and RHS.

Defines rule #3.

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

[3] aba=bbbb

Simplify [1] aba=aab.

Reduce RHS:

[2](aa)b
⇒ bbbb

Defines rule #4.

Referenced by [5].

[4] bbba=abbb

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

a a aa

Critical pair: abbb=bbba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] babbb=abbbb

Overlap of [3] aba=bbbb with [2] aa=bbb:

ab a aa

Critical pair: abbbb=bbbba.

Reduce RHS:

[4]b(bbba)
⇒ babbb

Flip LHS and RHS.

Defines rule #1.