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

Completion settings:

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

Axiom: abaaaaba=ab.

Referenced by [3].

Axiom: ab=c.

Defines rule #6.

Referenced by [3], [4], [5], [15].

Simplify [1] abaaaaba=ab.

Reduce RHS:

Referenced by [4].

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

Critical pair: caaaaba=c.

Reduce LHS:

Referenced by [5], [6], [8], [9], [11].

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

Critical pair: caaacc=cb.

Flip LHS and RHS.

Referenced by [7].

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

Critical pair: caaac=caaca.

Referenced by [7], [8], [9], [11], [12], [13], [17], [18].

Simplify [5] cb=caaacc.

Reduce RHS:

Referenced by [17].

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

Critical pair: caacaa=c.

Referenced by [9], [10].

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

Critical pair: caaacaaca=caac.

Reduce LHS:

Flip LHS and RHS.

Referenced by [10], [11], [12], [13], [17], [18], [19].

Simplify [8] caacaa=c.

Reduce LHS:

Referenced by [11], [12], [13], [14].

Overlap of [4] caaaca=c with [10] cacaaa=c:

Critical pair: caaac=ccaaa.

Reduce LHS:

Referenced by [12], [13].

Overlap of [10] cacaaa=c with [6] caaac=caaca:

Critical pair: cacaaca=cc.

Reduce LHS:

Referenced by [13], [16].

Overlap of [9] caac=caca with [10] cacaaa=c:

Critical pair: caac=cacaacaaa.

Reduce LHS:

Reduce RHS:

Referenced by [14], [15], [16].

Overlap of [10] cacaaa=c with [13] caca=ccaa:

Critical pair: ccaaaa=c.

Defines rule #4.

Referenced by [16].

Overlap of [13] caca=ccaa with [2] ab=c:

Critical pair: cacc=ccaab.

Reduce RHS:

Referenced by [16].

Overlap of [15] cacc=ccac with [14] ccaaaa=c:

Critical pair: cac=ccacaaaa.

Reduce RHS:

Defines rule #1.

Referenced by [17], [18], [19].

Simplify [7] cb=caacac.

Reduce RHS:

Defines rule #5.

Simplify [6] caaac=caaca.

Reduce RHS:

Defines rule #3.

Simplify [9] caac=caca.

Reduce RHS:

Defines rule #2.