Certificate for #13164 ⟨a, b | aba=aab, baa=ba⟩

Completion settings:

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

Axiom: aba=aab.

Referenced by [4].

Axiom: baa=ba.

Referenced by [5].

Axiom: ba=c.

Defines rule #3.

Referenced by [4], [5], [6], [7], [8].

Overlap of [1] aba=aab with [3] ba=c:

Critical pair: ac=aab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [7], [8].

Simplify [2] baa=ba.

Reduce RHS:

Referenced by [6].

Overlap of [5] baa=c with [3] ba=c:

Critical pair: ca=c.

Defines rule #1.

Referenced by [7], [8].

Overlap of [3] ba=c with [4] aab=ac:

Critical pair: bac=cab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [4] aab=ac with [3] ba=c:

Critical pair: aac=aca.

Reduce RHS:

Defines rule #4.