Certificate for #9375 ⟨a, b | ab=a, bbba=bbb⟩

Back:⟨a, b | ab=a, bbba=bbb⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #2.

Referenced by [3], [4].

[2] bbba=bbb

Axiom: bbba=bbb.

Defines rule #3.

Referenced by [3], [4].

[3] aa=a

Overlap of [1] ab=a with [2] bbba=bbb:

a b bbba

Critical pair: abbb=abba.

Reduce LHS:

[1](ab)bb
[1]⇒ (ab)b
[1]⇒ (ab)
⇒ a

Reduce RHS:

[1](ab)ba
[1]⇒ (ab)a
⇒ aa

Flip LHS and RHS.

Defines rule #1.

[4] bbbb=bbb

Overlap of [2] bbba=bbb with [1] ab=a:

bbb a ab

Critical pair: bbba=bbbb.

Reduce LHS:

[2](bbba)
⇒ bbb

Flip LHS and RHS.

Defines rule #4.