Certificate for #12671 ⟨a, b | aab=aaa, bbbbb=1⟩

Back:⟨a, b | aab=aaa, bbbbb=1⟩

Completion settings:

[1] aab=aaa

Axiom: aab=aaa.

Defines rule #1.

Referenced by [3].

[2] bbbbb=1

Axiom: bbbbb=1.

Defines rule #2.

Referenced by [3].

[3] aaaaaaa=aa

Overlap of [1] aab=aaa with [2] bbbbb=1:

aa b bbbbb

Critical pair: aa=aaabbbb.

Reduce RHS:

[1]a(aab)bbb
[1]⇒ aa(aab)bb
[1]⇒ aaa(aab)b
[1]⇒ aaaa(aab)
⇒ aaaaaaa

Flip LHS and RHS.

Defines rule #3.