Certificate for #22792 ⟨a, b | aaa=1, ababa=bab⟩

Completion settings:

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

Axiom: aaa=1.

Defines rule #1.

Referenced by [6], [8].

Axiom: ababa=bab.

Referenced by [4].

Axiom: bab=c.

Defines rule #4.

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

Simplify [2] ababa=bab.

Reduce RHS:

Referenced by [5].

Overlap of [4] ababa=c with [3] bab=c:

Critical pair: aca=c.

Referenced by [6].

Overlap of [5] aca=c with [1] aaa=1:

Critical pair: ac=caa.

Defines rule #2.

Referenced by [7].

Overlap of [3] bab=c with [3] bab=c:

Critical pair: bac=cab.

Reduce LHS:

Referenced by [8].

Overlap of [7] bcaa=cab with [1] aaa=1:

Critical pair: bc=caba.

Defines rule #3.