Certificate for #4230 ⟨a, b | abaaaaaba=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: abaaaaaba=ab.

Referenced by [3].

Axiom: ab=c.

Defines rule #6.

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

Simplify [1] abaaaaaba=ab.

Reduce RHS:

Referenced by [4].

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

Critical pair: caaaaaba=c.

Reduce LHS:

Defines rule #5.

Referenced by [5], [6], [7], [8], [9].

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

Critical pair: caaaacc=cb.

Flip LHS and RHS.

Defines rule #7.

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

Critical pair: caaaac=caaaca.

Flip LHS and RHS.

Defines rule #4.

Referenced by [7], [8].

Overlap of [4] caaaaca=c with [6] caaaca=caaaac:

Critical pair: caaaacaaaac=caaca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Overlap of [6] caaaca=caaaac with [6] caaaca=caaaac:

Critical pair: caaacaaaac=caaaacaaca.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [9].

Overlap of [4] caaaaca=c with [8] caca=caac:

Critical pair: caaaacaac=cca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.