Certificate for #25112 ⟨a, b | ab=a, bbbbbb=aa⟩

Back:⟨a, b | ab=a, bbbbbb=aa⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3], [4].

[2] bbbbbb=aa

Axiom: bbbbbb=aa.

Defines rule #4.

Referenced by [3], [4].

[3] aaa=a

Overlap of [1] ab=a with [2] bbbbbb=aa:

a b bbbbbb

Critical pair: aaa=abbbbb.

Reduce RHS:

[1](ab)bbbb
[1]⇒ (ab)bbb
[1]⇒ (ab)bb
[1]⇒ (ab)b
[1]⇒ (ab)
⇒ a

Defines rule #3.

Referenced by [5].

[4] baa=aa

Overlap of [2] bbbbbb=aa with [2] bbbbbb=aa:

b bbbbb bbbbbb

Critical pair: baa=aab.

Reduce RHS:

[1]a(ab)
⇒ aa

Referenced by [5].

[5] ba=a

Overlap of [4] baa=aa with [3] aaa=a:

b aa aaa

Critical pair: ba=aaa.

Reduce RHS:

[3](aaa)
⇒ a

Defines rule #2.