Certificate for #5847 ⟨a, b, c | ab=a, bab=bc⟩

Back:⟨a, b, c | ab=a, bab=bc⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [2], [3].

[2] bc=ba

Axiom: bab=bc.

Reduce LHS:

[1]b(ab)
⇒ ba

Flip LHS and RHS.

Defines rule #3.

Referenced by [3].

[3] ac=aa

Overlap of [1] ab=a with [2] bc=ba:

a b bc

Critical pair: aba=ac.

Reduce LHS:

[1](ab)a
⇒ aa

Flip LHS and RHS.

Defines rule #2.