Certificate for #7114 ⟨a, b | ab=aa, bbbb=aa⟩

Back:⟨a, b | ab=aa, bbbb=aa⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3], [4].

[2] bbbb=aa

Axiom: bbbb=aa.

Defines rule #3.

Referenced by [3], [4].

[3] aaaaa=aaa

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

a b bbbb

Critical pair: aaa=aabbb.

Reduce RHS:

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

Flip LHS and RHS.

Defines rule #4.

[4] baa=aaa

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

b bbb bbbb

Critical pair: baa=aab.

Reduce RHS:

[1]a(ab)
⇒ aaa

Defines rule #2.