Certificate for #16418 ⟨a, b | aba=ab, babb=ab⟩

Back:⟨a, b | aba=ab, babb=ab⟩

Completion settings:

[1] aba=ab

Axiom: aba=ab.

Defines rule #2.

Referenced by [3], [4].

[2] babb=ab

Axiom: babb=ab.

Referenced by [3], [4], [6], [7].

[3] abbb=aab

Overlap of [1] aba=ab with [2] babb=ab:

a ba babb

Critical pair: aab=abbb.

Flip LHS and RHS.

Referenced by [4], [5].

[4] aab=ab

Overlap of [2] babb=ab with [2] babb=ab:

bab b babb

Critical pair: babab=ababb.

Reduce LHS:

[1]b(aba)b
[2]⇒ (babb)
⇒ ab

Reduce RHS:

[1](aba)bb
[3]⇒ (abbb)
⇒ aab

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[5] abbb=ab

Simplify [3] abbb=aab.

Reduce RHS:

[4](aab)
⇒ ab

Referenced by [6].

[6] abb=bab

Overlap of [2] babb=ab with [5] abbb=ab:

b abb abbb

Critical pair: bab=abb.

Flip LHS and RHS.

Defines rule #1.

Referenced by [7].

[7] bbab=ab

Overlap of [2] babb=ab with [6] abb=bab:

b abb abb

Critical pair: bbab=ab.

Defines rule #4.