Certificate for #7315 ⟨a, b, c | ab=1, aaca=ac⟩

Completion settings:

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

Axiom: ab=1.

Defines rule #1.

Referenced by [6].

Axiom: aaca=ac.

Referenced by [4].

Axiom: ac=d.

Defines rule #5.

Referenced by [4], [5], [7].

Simplify [2] aaca=ac.

Reduce RHS:

Referenced by [5].

Overlap of [4] aaca=d with [3] ac=d:

Critical pair: ada=d.

Defines rule #3.

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

Overlap of [5] ada=d with [1] ab=1:

Critical pair: ad=db.

Flip LHS and RHS.

Defines rule #2.

Overlap of [5] ada=d with [3] ac=d:

Critical pair: add=dc.

Flip LHS and RHS.

Defines rule #6.

Overlap of [5] ada=d with [5] ada=d:

Critical pair: add=dda.

Flip LHS and RHS.

Defines rule #4.