Certificate for #5587 ⟨a, b, c | ab=c, bcac=c⟩

Completion settings:

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

Axiom: ab=c.

Defines rule #3.

Referenced by [5].

Axiom: bcac=c.

Referenced by [4].

Axiom: ac=d.

Defines rule #4.

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

Overlap of [2] bcac=c with [3] ac=d:

Critical pair: bcd=c.

Defines rule #1.

Referenced by [5].

Overlap of [1] ab=c with [4] bcd=c:

Critical pair: ac=ccd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [6].

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

Critical pair: ad=dcd.

Defines rule #5.