Certificate for #20844 ⟨a, b | ab=aa, bbbbb=aa⟩

Back:⟨a, b | ab=aa, bbbbb=aa⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3], [4].

[2] bbbbb=aa

Axiom: bbbbb=aa.

Defines rule #3.

Referenced by [3], [4].

[3] aaaaaa=aaa

Overlap of [1] ab=aa with [2] bbbbb=aa:

a b bbbbb

Critical pair: aaa=aabbbb.

Reduce RHS:

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

Flip LHS and RHS.

Defines rule #4.

[4] baa=aaa

Overlap of [2] bbbbb=aa with [2] bbbbb=aa:

b bbbb bbbbb

Critical pair: baa=aab.

Reduce RHS:

[1]a(ab)
⇒ aaa

Defines rule #2.