Certificate for #6034 ⟨a, b, c | ab=c, aca=ac⟩

Completion settings:

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

Axiom: ab=c.

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=c:

Critical pair: dc=db.

Referenced by [7], [8].

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

Critical pair: dd=dc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [8].

Simplify [6] dc=db.

Reduce RHS:

Defines rule #5.