Certificate for #9382 ⟨a, b | ab=a, bbbb=bba⟩

Back:⟨a, b | ab=a, bbbb=bba⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #2.

Referenced by [3], [4].

[2] bbbb=bba

Axiom: bbbb=bba.

Defines rule #4.

Referenced by [3], [4].

[3] aa=a

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

a b bbbb

Critical pair: abba=abbb.

Reduce LHS:

[1](ab)ba
[1]⇒ (ab)a
⇒ aa

Reduce RHS:

[1](ab)bb
[1]⇒ (ab)b
[1]⇒ (ab)
⇒ a

Defines rule #1.

[4] bbba=bba

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

b bbb bbbb

Critical pair: bbba=bbab.

Reduce RHS:

[1]bb(ab)
⇒ bba

Defines rule #3.