Certificate for #5864 ⟨a, b, c | ab=a, bba=cc⟩

Back:⟨a, b, c | ab=a, bba=cc⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [4].

[2] cc=bba

Axiom: bba=cc.

Flip LHS and RHS.

Defines rule #4.

Referenced by [3].

[3] bbac=cbba

Overlap of [2] cc=bba with [2] cc=bba:

c c cc

Critical pair: cbba=bbac.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4].

[4] aac=acbba

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

a b bbac

Critical pair: acbba=abac.

Reduce RHS:

[1](ab)ac
⇒ aac

Flip LHS and RHS.

Defines rule #2.