Certificate for #6535 ⟨a, b | aaa=a, aaba=ba⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #1.

Referenced by [6].

Axiom: aaba=ba.

Referenced by [4].

Axiom: ba=c.

Defines rule #4.

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

Simplify [2] aaba=ba.

Reduce RHS:

Referenced by [5].

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

Critical pair: aac=c.

Defines rule #2.

Referenced by [7].

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

Critical pair: ba=caa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

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

Critical pair: bc=cac.

Defines rule #5.