Certificate for #16351 ⟨a, b | aba=aa, aabb=bb⟩

Back:⟨a, b | aba=aa, aabb=bb⟩

Completion settings:

[1] aba=aa

Axiom: aba=aa.

Defines rule #1.

Referenced by [3], [4].

[2] aabb=bb

Axiom: aabb=bb.

Defines rule #3.

Referenced by [3], [4].

[3] abbb=abb

Overlap of [1] aba=aa with [2] aabb=bb:

ab a aabb

Critical pair: abbb=aaabb.

Reduce RHS:

[2]a(aabb)
⇒ abb

Referenced by [4].

[4] bbb=bb

Overlap of [1] aba=aa with [3] abbb=abb:

ab a abbb

Critical pair: ababb=aabbb.

Reduce LHS:

[1](aba)bb
[2]⇒ (aabb)
⇒ bb

Reduce RHS:

[2](aabb)b
⇒ bbb

Flip LHS and RHS.

Defines rule #2.