Certificate for #5884 ⟨a, b, c | ab=a, bca=bc⟩

Completion settings:

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

Axiom: ab=a.

Defines rule #6.

Referenced by [6], [7].

Axiom: bca=bc.

Referenced by [4].

Axiom: bc=d.

Defines rule #4.

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

Simplify [2] bca=bc.

Reduce RHS:

Referenced by [5].

Overlap of [4] bca=d with [3] bc=d:

Critical pair: da=d.

Defines rule #3.

Referenced by [7].

Overlap of [1] ab=a with [3] bc=d:

Critical pair: ad=ac.

Flip LHS and RHS.

Defines rule #5.

Overlap of [5] da=d with [1] ab=a:

Critical pair: da=db.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [8].

Overlap of [7] db=d with [3] bc=d:

Critical pair: dd=dc.

Flip LHS and RHS.

Defines rule #1.