Certificate for #25656 ⟨a, b | ab=a, bbbbb=baa⟩

Back:⟨a, b | ab=a, bbbbb=baa⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3], [4].

[2] bbbbb=baa

Axiom: bbbbb=baa.

Defines rule #4.

Referenced by [3], [4].

[3] aaa=a

Overlap of [1] ab=a with [2] bbbbb=baa:

a b bbbbb

Critical pair: abaa=abbbb.

Reduce LHS:

[1](ab)aa
⇒ aaa

Reduce RHS:

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

Defines rule #2.

Referenced by [5].

[4] bbaa=baa

Overlap of [2] bbbbb=baa with [2] bbbbb=baa:

b bbbb bbbbb

Critical pair: bbaa=baab.

Reduce RHS:

[1]ba(ab)
⇒ baa

Referenced by [5].

[5] bba=ba

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

bb aa aaa

Critical pair: bba=baaa.

Reduce RHS:

[3]b(aaa)
⇒ ba

Defines rule #3.