Certificate for #3009 ⟨a, b | aa=a, aaba=ba⟩

Completion settings:

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

Axiom: aa=a.

Defines rule #1.

Referenced by [2], [6].

Axiom: aaba=ba.

Reduce LHS:

Referenced by [4].

Axiom: ba=c.

Defines rule #4.

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

Simplify [2] aba=ba.

Reduce RHS:

Referenced by [5].

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

Critical pair: ac=c.

Defines rule #2.

Referenced by [7].

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

Critical pair: ba=ca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

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

Critical pair: bc=cc.

Defines rule #5.