Certificate for #15971 ⟨a, b | aaa=aa, baab=aa⟩

Back:⟨a, b | aaa=aa, baab=aa⟩

Completion settings:

[1] aaa=aa

Axiom: aaa=aa.

Defines rule #1.

Referenced by [3], [5].

[2] baab=aa

Axiom: baab=aa.

Referenced by [3], [4].

[3] baa=aab

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

baa b baab

Critical pair: baaaa=aaaab.

Reduce LHS:

[1]b(aaa)a
[1]⇒ b(aaa)
⇒ baa

Reduce RHS:

[1](aaa)ab
[1]⇒ (aaa)b
⇒ aab

Defines rule #2.

Referenced by [4], [5].

[4] aabb=aa

Overlap of [2] baab=aa with [3] baa=aab:

baab baa

Critical pair: aabb=aa.

Defines rule #4.

[5] aaba=aab

Overlap of [3] baa=aab with [1] aaa=aa:

b aa aaa

Critical pair: baa=aaba.

Reduce LHS:

[3](baa)
⇒ aab

Flip LHS and RHS.

Defines rule #3.