Certificate for #1036 ⟨a, b, c | ab=c, bac=c⟩

Completion settings:

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

Axiom: ab=c.

Referenced by [5], [6].

Axiom: bac=c.

Referenced by [4].

Axiom: ac=d.

Referenced by [4], [5].

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

Critical pair: bd=c.

Flip LHS and RHS.

Defines rule #2.

Referenced by [5], [6].

Overlap of [3] ac=d with [4] c=bd:

Critical pair: abd=d.

Reduce LHS:

Defines rule #1.

Referenced by [7].

Simplify [1] ab=c.

Reduce RHS:

Defines rule #3.

Referenced by [7].

Overlap of [6] ab=bd with [5] bdd=d:

Critical pair: ad=bddd.

Reduce RHS:

Defines rule #4.