Certificate for #19538 ⟨a, b | aab=b, abaaa=ba⟩

Back:⟨a, b | aab=b, abaaa=ba⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #3.

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

[2] abaaa=ba

Axiom: abaaa=ba.

Referenced by [3], [4].

[3] aba=baaa

Overlap of [1] aab=b with [2] abaaa=ba:

a ab abaaa

Critical pair: aba=baaa.

Defines rule #2.

Referenced by [5].

[4] abb=bb

Overlap of [2] abaaa=ba with [1] aab=b:

abaa a aab

Critical pair: abaab=baab.

Reduce LHS:

[1]ab(aab)
⇒ abb

Reduce RHS:

[1]b(aab)
⇒ bb

Defines rule #4.

[5] baaaaa=ba

Overlap of [1] aab=b with [3] aba=baaa:

a ab aba

Critical pair: abaaa=ba.

Reduce LHS:

[3](aba)aa
⇒ baaaaa

Defines rule #1.