Certificate for #7418 ⟨a, b, c | ab=1, acba=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.

Axiom: acba=ac.

Referenced by [4].

Axiom: ac=d.

Defines rule #3.

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

Simplify [2] acba=ac.

Reduce RHS:

Referenced by [5].

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

Critical pair: dba=d.

Defines rule #2.

Referenced by [6].

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

Critical pair: dbd=dc.

Flip LHS and RHS.

Defines rule #4.