Certificate for #3319 ⟨a, b, c | ab=aa, aca=c⟩

Back:⟨a, b, c | ab=aa, aca=c⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #1.

Referenced by [3].

[2] aca=c

Axiom: aca=c.

Defines rule #3.

Referenced by [3], [4].

[3] cb=ca

Overlap of [2] aca=c with [1] ab=aa:

ac a ab

Critical pair: acaa=cb.

Reduce LHS:

[2](aca)a
⇒ ca

Flip LHS and RHS.

Defines rule #2.

[4] cca=acc

Overlap of [2] aca=c with [2] aca=c:

ac a aca

Critical pair: acc=cca.

Flip LHS and RHS.

Defines rule #4.