Certificate for #25603 ⟨a, b | ab=a, bbaaa=bbb⟩

Back:⟨a, b | ab=a, bbaaa=bbb⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #2.

Referenced by [3].

[2] bbb=bbaaa

Axiom: bbaaa=bbb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3].

[3] aaaa=a

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

a b bbb

Critical pair: abbaaa=abb.

Reduce LHS:

[1](ab)baaa
[1]⇒ (ab)aaa
⇒ aaaa

Reduce RHS:

[1](ab)b
[1]⇒ (ab)
⇒ a

Defines rule #1.