Certificate for #5424 ⟨a, b, c | ab=a, caca=c⟩

Back:⟨a, b, c | ab=a, caca=c⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3].

[2] caca=c

Axiom: caca=c.

Defines rule #4.

Referenced by [3], [4].

[3] cb=c

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

cac a ab

Critical pair: caca=cb.

Reduce LHS:

[2](caca)
⇒ c

Flip LHS and RHS.

Defines rule #2.

[4] cca=cac

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

ca ca caca

Critical pair: cac=cca.

Flip LHS and RHS.

Defines rule #3.