Certificate for #5816 ⟨a, b, c | ab=a, aca=ac⟩

Completion settings:

• Auxiliary generators:
  1. d = ac
• Reduction order:
  • Left-to-right shortlex with a < b < d < c

Axiom: ab=a.

Defines rule #1.

Referenced by [6].

Axiom: aca=ac.

Referenced by [4].

Axiom: ac=d.

Defines rule #2.

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

Simplify [2] aca=ac.

Reduce RHS:

Referenced by [5].

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

Critical pair: da=d.

Defines rule #3.

Referenced by [6], [7].

Overlap of [5] da=d with [1] ab=a:

Critical pair: da=db.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

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

Critical pair: dd=dc.

Flip LHS and RHS.

Defines rule #5.