Certificate for #6821 ⟨a, b | aab=b, bab=aaa⟩

Back:⟨a, b | aab=b, bab=aaa⟩

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #1.

Referenced by [3], [4].

[2] bab=aaa

Axiom: bab=aaa.

Defines rule #3.

Referenced by [3], [4].

[3] aaaaa=aaa

Overlap of [1] aab=b with [2] bab=aaa:

aa b bab

Critical pair: aaaaa=bab.

Reduce RHS:

[2](bab)
⇒ aaa

Defines rule #4.

Referenced by [5].

[4] baaaa=b

Overlap of [2] bab=aaa with [2] bab=aaa:

ba b bab

Critical pair: baaaa=aaaab.

Reduce RHS:

[1]aa(aab)
[1]⇒ (aab)
⇒ b

Referenced by [5], [6].

[5] baaa=ba

Overlap of [4] baaaa=b with [3] aaaaa=aaa:

b aaaa aaaaa

Critical pair: baaa=ba.

Referenced by [6].

[6] baa=b

Overlap of [4] baaaa=b with [5] baaa=ba:

baaaa baaa

Critical pair: baa=b.

Defines rule #2.