Certificate for #402 ⟨a, b, c | abc=a, cbc=1⟩

Completion settings:

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

Axiom: abc=a.

Referenced by [5], [6].

Axiom: cbc=1.

Referenced by [3], [4].

Overlap of [2] cbc=1 with [2] cbc=1:

Critical pair: cb=bc.

Defines rule #3.

Referenced by [4], [6].

Overlap of [2] cbc=1 with [3] cb=bc:

Critical pair: bcc=1.

Defines rule #4.

Referenced by [5].

Overlap of [1] abc=a with [4] bcc=1:

Critical pair: a=ac.

Flip LHS and RHS.

Defines rule #2.

Referenced by [6].

Overlap of [5] ac=a with [3] cb=bc:

Critical pair: abc=ab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.