Certificate for #3063 ⟨a, b, c | abc=a, bca=b⟩

Completion settings:

• Reduction order:
  • Left-to-right shortlex with a < b < c

Axiom: abc=a.

Referenced by [3], [4].

Axiom: bca=b.

Defines rule #5.

Referenced by [3], [5], [6].

Overlap of [1] abc=a with [2] bca=b:

Critical pair: ab=aa.

Defines rule #1.

Referenced by [4], [5].

Overlap of [1] abc=a with [3] ab=aa:

Critical pair: aac=a.

Defines rule #3.

Referenced by [6].

Overlap of [2] bca=b with [3] ab=aa:

Critical pair: bcaa=bb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [2] bca=b with [4] aac=a:

Critical pair: bca=bac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.