Certificate for #1697 ⟨a, b | bab=ab, bbb=b⟩

Completion settings:

• Auxiliary generators:
  1. c = ab
• Reduction order:
  • Left-to-right shortlex with c < a < b

Axiom: bab=ab.

Referenced by [4].

Axiom: bbb=b.

Defines rule #5.

Referenced by [7].

Axiom: ab=c.

Defines rule #2.

Referenced by [4], [5], [6], [7].

Simplify [1] bab=ab.

Reduce RHS:

Referenced by [5].

Overlap of [4] bab=c with [3] ab=c:

Critical pair: bc=c.

Defines rule #3.

Referenced by [6].

Overlap of [3] ab=c with [5] bc=c:

Critical pair: ac=cc.

Defines rule #1.

Overlap of [3] ab=c with [2] bbb=b:

Critical pair: ab=cbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.