Certificate for #6071 ⟨a, b, c | ab=c, bac=ca⟩

Completion settings:

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

Axiom: ab=c.

Defines rule #2.

Referenced by [5], [7].

Axiom: bac=ca.

Referenced by [4].

Axiom: ac=d.

Defines rule #1.

Referenced by [4], [5], [6], [8].

Overlap of [2] bac=ca with [3] ac=d:

Critical pair: bd=ca.

Defines rule #4.

Referenced by [5].

Overlap of [1] ab=c with [4] bd=ca:

Critical pair: aca=cd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [6].

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

Critical pair: ada=dd.

Defines rule #6.

Referenced by [7], [8].

Overlap of [6] ada=dd with [1] ab=c:

Critical pair: adc=ddb.

Defines rule #7.

Overlap of [6] ada=dd with [3] ac=d:

Critical pair: add=ddc.

Defines rule #5.