Certificate for #1019 ⟨a, b | ab=a, bba=bb⟩

Back:⟨a, b | ab=a, bba=bb⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #2.

Referenced by [3], [4].

[2] bba=bb

Axiom: bba=bb.

Defines rule #3.

Referenced by [3], [4].

[3] aa=a

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

a b bba

Critical pair: abb=aba.

Reduce LHS:

[1](ab)b
[1]⇒ (ab)
⇒ a

Reduce RHS:

[1](ab)a
⇒ aa

Flip LHS and RHS.

Defines rule #1.

[4] bbb=bb

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

bb a ab

Critical pair: bba=bbb.

Reduce LHS:

[2](bba)
⇒ bb

Flip LHS and RHS.

Defines rule #4.