Certificate for #16427 ⟨a, b | aba=ab, bbab=ba⟩

Back:⟨a, b | aba=ab, bbab=ba⟩

Completion settings:

[1] aba=ab

Axiom: aba=ab.

Defines rule #1.

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

[2] bbab=ba

Axiom: bbab=ba.

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

[3] baa=ba

Overlap of [2] bbab=ba with [1] aba=ab:

bb ab aba

Critical pair: bbab=baa.

Reduce LHS:

[2](bbab)
⇒ ba

Flip LHS and RHS.

Defines rule #2.

Referenced by [4].

[4] babb=ba

Overlap of [2] bbab=ba with [2] bbab=ba:

bba b bbab

Critical pair: bbaba=babab.

Reduce LHS:

[2](bbab)a
[3]⇒ (baa)
⇒ ba

Reduce RHS:

[1]b(aba)b
⇒ babb

Flip LHS and RHS.

Defines rule #5.

Referenced by [5], [6].

[5] abbb=ab

Overlap of [1] aba=ab with [4] babb=ba:

a ba babb

Critical pair: aba=abbb.

Reduce LHS:

[1](aba)
⇒ ab

Flip LHS and RHS.

Defines rule #4.

[6] bba=bab

Overlap of [2] bbab=ba with [4] babb=ba:

b bab babb

Critical pair: bba=bab.

Defines rule #3.