Certificate for #2256 ⟨a, b | ab=aa, bbb=aa⟩

Back:⟨a, b | ab=aa, bbb=aa⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3], [4].

[2] bbb=aa

Axiom: bbb=aa.

Defines rule #3.

Referenced by [3], [4].

[3] aaaa=aaa

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

a b bbb

Critical pair: aaa=aabb.

Reduce RHS:

[1]a(ab)b
[1]⇒ aa(ab)
⇒ aaaa

Flip LHS and RHS.

Defines rule #4.

[4] baa=aaa

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

b bb bbb

Critical pair: baa=aab.

Reduce RHS:

[1]a(ab)
⇒ aaa

Defines rule #2.