Certificate for #3424 ⟨a, b, c | ba=ab, aca=c⟩

Completion settings:

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

Axiom: ba=ab.

Referenced by [4].

Axiom: aca=c.

Defines rule #6.

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

Axiom: ab=d.

Defines rule #2.

Referenced by [4], [5], [6], [9].

Simplify [1] ba=ab.

Reduce RHS:

Defines rule #4.

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

Overlap of [4] ba=d with [3] ab=d:

Critical pair: bd=db.

Defines rule #3.

Overlap of [3] ab=d with [4] ba=d:

Critical pair: ad=da.

Defines rule #1.

Overlap of [4] ba=d with [2] aca=c:

Critical pair: bc=dca.

Defines rule #7.

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

Critical pair: acc=cca.

Defines rule #8.

Overlap of [2] aca=c with [3] ab=d:

Critical pair: acd=cb.

Defines rule #5.