Certificate for #5911 ⟨a, b, c | ab=a, caa=bc⟩

Completion settings:

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

Axiom: ab=a.

Defines rule #1.

Referenced by [4], [5].

Axiom: caa=bc.

Flip LHS and RHS.

Defines rule #5.

Referenced by [4].

Axiom: ac=d.

Defines rule #4.

Referenced by [4], [6].

Overlap of [1] ab=a with [2] bc=caa:

Critical pair: acaa=ac.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Referenced by [5], [6].

Overlap of [4] daa=d with [1] ab=a:

Critical pair: daa=db.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [4] daa=d with [3] ac=d:

Critical pair: dad=dc.

Flip LHS and RHS.

Defines rule #6.