Certificate for #110 ⟨a, b | abab=ba⟩

Completion settings:

• Auxiliary generators:
  1. c = ba
• Reduction order:
  • Left-to-right recursive path with deg(b) = deg(c) = 0, b < c; deg(a) = 1

Axiom: abab=ba.

Referenced by [3].

Axiom: ba=c.

Defines rule #3.

Referenced by [3], [4], [5], [6].

Simplify [1] abab=ba.

Reduce RHS:

Referenced by [4].

Overlap of [3] abab=c with [2] ba=c:

Critical pair: acb=c.

Defines rule #2.

Referenced by [5], [6].

Overlap of [2] ba=c with [4] acb=c:

Critical pair: bc=ccb.

Flip LHS and RHS.

Defines rule #1.

Overlap of [4] acb=c with [2] ba=c:

Critical pair: acc=ca.

Flip LHS and RHS.

Defines rule #4.