Certificate for #3134 ⟨a, b | ab=a, bbbb=ba⟩

Back:⟨a, b | ab=a, bbbb=ba⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #2.

Referenced by [3], [4].

[2] bbbb=ba

Axiom: bbbb=ba.

Defines rule #4.

Referenced by [3], [4].

[3] aa=a

Overlap of [1] ab=a with [2] bbbb=ba:

a b bbbb

Critical pair: aba=abbb.

Reduce LHS:

[1](ab)a
⇒ aa

Reduce RHS:

[1](ab)bb
[1]⇒ (ab)b
[1]⇒ (ab)
⇒ a

Defines rule #1.

[4] bba=ba

Overlap of [2] bbbb=ba with [2] bbbb=ba:

b bbb bbbb

Critical pair: bba=bab.

Reduce RHS:

[1]b(ab)
⇒ ba

Defines rule #3.