Certificate for #158 ⟨a, b | ab=aa, ba=b⟩

Back:⟨a, b | ab=aa, ba=b⟩

Completion settings:

[1] aa=ab

Axiom: ab=aa.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3].

[2] ba=b

Axiom: ba=b.

Defines rule #2.

Referenced by [3].

[3] bb=b

Overlap of [2] ba=b with [1] aa=ab:

b a aa

Critical pair: bab=ba.

Reduce LHS:

[2](ba)b
⇒ bb

Reduce RHS:

[2](ba)
⇒ b

Defines rule #1.