Certificate for #955 ⟨a, b, c | ab=a, aca=c⟩

Back:⟨a, b, c | ab=a, aca=c⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3].

[2] aca=c

Axiom: aca=c.

Defines rule #3.

Referenced by [3], [4].

[3] cb=c

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

ac a ab

Critical pair: aca=cb.

Reduce LHS:

[2](aca)
⇒ c

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.