Certificate for #5941 ⟨a, b, c | ab=a, cba=cc⟩

Back:⟨a, b, c | ab=a, cba=cc⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3].

[2] cba=cc

Axiom: cba=cc.

Defines rule #4.

Referenced by [3], [4].

[3] ccb=cc

Overlap of [2] cba=cc with [1] ab=a:

cb a ab

Critical pair: cba=ccb.

Reduce LHS:

[2](cba)
⇒ cc

Flip LHS and RHS.

Defines rule #3.

Referenced by [4].

[4] cca=ccc

Overlap of [3] ccb=cc with [2] cba=cc:

c cb cba

Critical pair: ccc=cca.

Flip LHS and RHS.

Defines rule #2.