Certificate for #16401 ⟨a, b | aba=ab, abbb=aa⟩

Back:⟨a, b | aba=ab, abbb=aa⟩

Completion settings:

[1] aba=ab

Axiom: aba=ab.

Defines rule #3.

Referenced by [3], [4].

[2] abbb=aa

Axiom: abbb=aa.

Defines rule #5.

Referenced by [4], [5].

[3] abba=abb

Overlap of [1] aba=ab with [1] aba=ab:

ab a aba

Critical pair: abab=abba.

Reduce LHS:

[1](aba)b
⇒ abb

Flip LHS and RHS.

Defines rule #4.

[4] aab=ab

Overlap of [1] aba=ab with [2] abbb=aa:

ab a abbb

Critical pair: abaa=abbbb.

Reduce LHS:

[1](aba)a
[1]⇒ (aba)
⇒ ab

Reduce RHS:

[2](abbb)b
⇒ aab

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] aaa=aa

Overlap of [4] aab=ab with [2] abbb=aa:

a ab abbb

Critical pair: aaa=abbb.

Reduce RHS:

[2](abbb)
⇒ aa

Defines rule #1.