Certificate for #3123 ⟨a, b | ab=a, bbaa=bb⟩

Back:⟨a, b | ab=a, bbaa=bb⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3], [4].

[2] bbaa=bb

Axiom: bbaa=bb.

Defines rule #4.

Referenced by [3], [4].

[3] aaa=a

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

a b bbaa

Critical pair: abb=abaa.

Reduce LHS:

[1](ab)b
[1]⇒ (ab)
⇒ a

Reduce RHS:

[1](ab)aa
⇒ aaa

Flip LHS and RHS.

Defines rule #2.

[4] bbb=bb

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

bba a ab

Critical pair: bbaa=bbb.

Reduce LHS:

[2](bbaa)
⇒ bb

Flip LHS and RHS.

Defines rule #3.