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] ba=bbbb

Axiom: bbbb=ba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3], [4].

[3] aa=a

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

a b ba

Critical pair: abbbb=aa.

Reduce LHS:

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

Flip LHS and RHS.

Defines rule #4.

[4] bbbbb=bbbb

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

b a ab

Critical pair: ba=bbbbb.

Reduce LHS:

[2](ba)
⇒ bbbb

Flip LHS and RHS.

Defines rule #1.