Certificate for #2024 ⟨a, b | abaaaaba=ab⟩

Completion settings:

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

Axiom: abaaaaba=ab.

Referenced by [3].

Axiom: ab=c.

Defines rule #5.

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

Simplify [1] abaaaaba=ab.

Reduce RHS:

Referenced by [4].

Overlap of [3] abaaaaba=c with [2] ab=c:

Critical pair: caaaaba=c.

Reduce LHS:

Defines rule #4.

Referenced by [5], [6], [7], [8].

Overlap of [4] caaaca=c with [2] ab=c:

Critical pair: caaacc=cb.

Flip LHS and RHS.

Defines rule #6.

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

Critical pair: caaac=caaca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [7], [8].

Overlap of [4] caaaca=c with [6] caaca=caaac:

Critical pair: caaacaaac=caca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [6] caaca=caaac with [6] caaca=caaac:

Critical pair: caacaaac=caaacaca.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.