Certificate for #7117 ⟨a, b | ab=aa, bbbb=bb⟩

Back:⟨a, b | ab=aa, bbbb=bb⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3].

[2] bbbb=bb

Axiom: bbbb=bb.

Defines rule #2.

Referenced by [3].

[3] aaaaa=aaa

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

a b bbbb

Critical pair: abb=aabbb.

Reduce LHS:

[1](ab)b
[1]⇒ a(ab)
⇒ aaa

Reduce RHS:

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

Flip LHS and RHS.

Defines rule #3.