Certificate for #3122 ⟨a, b | ab=a, bbaa=ba⟩

Back:⟨a, b | ab=a, bbaa=ba⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3].

[2] bbaa=ba

Axiom: bbaa=ba.

Referenced by [3], [4], [5].

[3] aaa=aa

Overlap of [1] ab=a with [2] bbaa=ba:

a b bbaa

Critical pair: aba=abaa.

Reduce LHS:

[1](ab)a
⇒ aa

Reduce RHS:

[1](ab)aa
⇒ aaa

Flip LHS and RHS.

Defines rule #2.

Referenced by [4].

[4] baa=ba

Overlap of [2] bbaa=ba with [3] aaa=aa:

bb aa aaa

Critical pair: bbaa=baa.

Reduce LHS:

[2](bbaa)
⇒ ba

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[5] bba=ba

Overlap of [2] bbaa=ba with [4] baa=ba:

b baa baa

Critical pair: bba=ba.

Defines rule #4.