Certificate for #3422 ⟨a, b, c | ba=ab, aca=a⟩

Completion settings:

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

Axiom: ba=ab.

Referenced by [4], [5], [8], [9].

Axiom: aca=a.

Defines rule #5.

Referenced by [4], [6].

Axiom: bca=d.

Defines rule #8.

Referenced by [4], [6], [7].

Overlap of [1] ba=ab with [2] aca=a:

Critical pair: ba=abca.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Referenced by [5], [7], [8], [9].

Overlap of [4] ab=ad with [1] ba=ab:

Critical pair: aab=ada.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Overlap of [3] bca=d with [2] aca=a:

Critical pair: bca=dca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Overlap of [3] bca=d with [4] ab=ad:

Critical pair: bcad=db.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [8].

Overlap of [7] db=dd with [1] ba=ab:

Critical pair: dab=dda.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Simplify [1] ba=ab.

Reduce RHS:

Defines rule #3.