Certificate for #21047 ⟨a, b | ab=aa, bbbb=bbb⟩

Back:⟨a, b | ab=aa, bbbb=bbb⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3].

[2] bbbb=bbb

Axiom: bbbb=bbb.

Defines rule #2.

Referenced by [3].

[3] aaaaa=aaaa

Overlap of [1] ab=aa with [2] bbbb=bbb:

a b bbbb

Critical pair: abbb=aabbb.

Reduce LHS:

[1](ab)bb
[1]⇒ a(ab)b
[1]⇒ aa(ab)
⇒ aaaa

Reduce RHS:

[1]a(ab)bb
[1]⇒ aa(ab)b
[1]⇒ aaa(ab)
⇒ aaaaa

Flip LHS and RHS.

Defines rule #3.