Certificate for #15954 ⟨a, b | aaa=aa, aaba=ba⟩

Completion settings:

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

Axiom: aaa=aa.

Defines rule #4.

Referenced by [6], [7].

Axiom: aaba=ba.

Referenced by [4].

Axiom: ba=c.

Defines rule #2.

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

Simplify [2] aaba=ba.

Reduce RHS:

Referenced by [5].

Overlap of [4] aaba=c with [3] ba=c:

Critical pair: aac=c.

Referenced by [6].

Overlap of [1] aaa=aa with [5] aac=c:

Critical pair: ac=aac.

Reduce RHS:

Defines rule #1.

Referenced by [8].

Overlap of [3] ba=c with [1] aaa=aa:

Critical pair: baa=caa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Overlap of [3] ba=c with [6] ac=c:

Critical pair: bc=cc.

Defines rule #3.