Certificate for #15974 ⟨a, b | aaa=aa, babb=aa⟩

Back:⟨a, b | aaa=aa, babb=aa⟩

Completion settings:

[1] aaa=aa

Axiom: aaa=aa.

Defines rule #1.

Referenced by [3], [4].

[2] babb=aa

Axiom: babb=aa.

Defines rule #4.

Referenced by [3].

[3] aabb=babaa

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

bab b babb

Critical pair: babaa=aaabb.

Reduce RHS:

[1](aaa)bb
⇒ aabb

Flip LHS and RHS.

Defines rule #3.

Referenced by [4].

[4] ababaa=babaa

Overlap of [1] aaa=aa with [3] aabb=babaa:

a aa aabb

Critical pair: ababaa=aabb.

Reduce RHS:

[3](aabb)
⇒ babaa

Defines rule #2.