Certificate for #2865 ⟨a, b, c | aab=a, aca=c⟩

Back:⟨a, b, c | aab=a, aca=c⟩

Completion settings:

[1] aab=a

Axiom: aab=a.

Defines rule #2.

Referenced by [3].

[2] aca=c

Axiom: aca=c.

Defines rule #3.

Referenced by [3], [4], [5].

[3] cab=c

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

ac a aab

Critical pair: aca=cab.

Reduce LHS:

[2](aca)
⇒ c

Flip LHS and RHS.

Defines rule #4.

Referenced by [5].

[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 #5.

[5] cb=ac

Overlap of [2] aca=c with [3] cab=c:

a ca cab

Critical pair: ac=cb.

Flip LHS and RHS.

Defines rule #1.