Certificate for #549 ⟨a, b | ababa=bab⟩

Completion settings:

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

Axiom: ababa=bab.

Referenced by [3].

Axiom: bab=c.

Defines rule #5.

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

Simplify [1] ababa=bab.

Reduce RHS:

Referenced by [4].

Overlap of [3] ababa=c with [2] bab=c:

Critical pair: aca=c.

Defines rule #1.

Referenced by [5], [7].

Overlap of [4] aca=c with [4] aca=c:

Critical pair: acc=cca.

Flip LHS and RHS.

Defines rule #2.

Overlap of [2] bab=c with [2] bab=c:

Critical pair: bac=cab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [7].

Overlap of [4] aca=c with [6] cab=bac:

Critical pair: abac=cb.

Flip LHS and RHS.

Defines rule #3.