Certificate for #3549 ⟨a, b, c | ab=aa, bc=bb⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3].

[2] bc=bb

Axiom: bc=bb.

Defines rule #2.

Referenced by [3].

[3] aac=aaa

Overlap of [1] ab=aa with [2] bc=bb:

a b bc

Critical pair: abb=aac.

Reduce LHS:

[1](ab)b
[1]⇒ a(ab)
⇒ aaa

Flip LHS and RHS.

Defines rule #3.