Certificate for #5697 ⟨a, b, c | aa=b, aca=ac⟩

Completion settings:

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

Axiom: aa=b.

Flip LHS and RHS.

Defines rule #4.

Axiom: aca=ac.

Referenced by [4].

Axiom: ac=d.

Defines rule #3.

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

Simplify [2] aca=ac.

Reduce RHS:

Referenced by [5].

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

Critical pair: da=d.

Defines rule #2.

Referenced by [6].

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

Critical pair: dd=dc.

Flip LHS and RHS.

Defines rule #1.