Certificate for #9110 ⟨a, b | ab=a, bbbbb=ba⟩

Back:⟨a, b | ab=a, bbbbb=ba⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #2.

Referenced by [3], [4].

[2] ba=bbbbb

Axiom: bbbbb=ba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4].

[3] aa=a

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

a b ba

Critical pair: abbbbb=aa.

Reduce LHS:

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

Flip LHS and RHS.

Defines rule #4.

[4] bbbbbb=bbbbb

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

b a ab

Critical pair: ba=bbbbbb.

Reduce LHS:

[2](ba)
⇒ bbbbb

Flip LHS and RHS.

Defines rule #1.