Certificate for #6104 ⟨a, b, c | ab=c, cac=ca⟩

Completion settings:

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

Axiom: ab=c.

Defines rule #5.

Referenced by [7].

Axiom: cac=ca.

Referenced by [4].

Axiom: ca=d.

Defines rule #3.

Referenced by [4], [5], [6], [7].

Simplify [2] cac=ca.

Reduce RHS:

Referenced by [5].

Overlap of [4] cac=d with [3] ca=d:

Critical pair: dc=d.

Defines rule #2.

Referenced by [6].

Overlap of [5] dc=d with [3] ca=d:

Critical pair: dd=da.

Flip LHS and RHS.

Defines rule #1.

Overlap of [3] ca=d with [1] ab=c:

Critical pair: cc=db.

Flip LHS and RHS.

Defines rule #4.