Certificate for #16131 ⟨a, b | aab=aa, bbaa=ba⟩

Completion settings:

Reduction order:
- Left-to-right shortlex with a < b

[1] aab=aa

Axiom: aab=aa.

Defines rule #1.

Referenced by [3], [4].

[2] bbaa=ba

Axiom: bbaa=ba.

Referenced by [3], [4], [5], [6], [7].

[3] aaaa=aaa

Overlap of [1] aab=aa with [2] bbaa=ba:

aa b bbaa

Critical pair: aaba=aabaa.

Reduce LHS:

[1]	(aab)a
	⇒ aaa

Reduce RHS:

[1]	(aab)aa
	⇒ aaaa

Flip LHS and RHS.

Defines rule #5.

[4] bab=ba

Overlap of [2] bbaa=ba with [1] aab=aa:

bb aa aab

Critical pair: bbaa=bab.

Reduce LHS:

[2]	(bbaa)
	⇒ ba

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[5] baaa=baa

Overlap of [4] bab=ba with [2] bbaa=ba:

ba b bbaa

Critical pair: baba=babaa.

Reduce LHS:

[4]	(bab)a
	⇒ baa

Reduce RHS:

[4]	(bab)aa
	⇒ baaa

Flip LHS and RHS.

Referenced by [6].

[6] baa=ba

Overlap of [2] bbaa=ba with [5] baaa=baa:

b baa baaa

Critical pair: bbaa=baa.

Reduce LHS:

[2]	(bbaa)
	⇒ ba

Flip LHS and RHS.

Defines rule #2.

Referenced by [7].

[7] bba=ba

Overlap of [2] bbaa=ba with [6] baa=ba:

b baa baa

Critical pair: bba=ba.

Defines rule #4.