Certificate for #5928 ⟨a, b, c | ab=a, cac=bb⟩

Back:⟨a, b, c | ab=a, cac=bb⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3], [4].

[2] cac=bb

Axiom: cac=bb.

Defines rule #2.

Referenced by [3].

[3] bbac=ca

Overlap of [2] cac=bb with [2] cac=bb:

ca c cac

Critical pair: cabb=bbac.

Reduce LHS:

[1]c(ab)b
[1]⇒ c(ab)
⇒ ca

Flip LHS and RHS.

Defines rule #4.

Referenced by [4].

[4] aac=aca

Overlap of [1] ab=a with [3] bbac=ca:

a b bbac

Critical pair: aca=abac.

Reduce RHS:

[1](ab)ac
⇒ aac

Flip LHS and RHS.

Defines rule #3.