Certificate for #4501 ⟨a, b, c | abc=1, aaca=c⟩

Completion settings:

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

Axiom: abc=1.

Defines rule #2.

Referenced by [3], [5].

Axiom: aaca=c.

Referenced by [3], [4].

Overlap of [2] aaca=c with [1] abc=1:

Critical pair: aac=cbc.

Defines rule #1.

Referenced by [4], [6].

Overlap of [2] aaca=c with [3] aac=cbc:

Critical pair: cbca=c.

Referenced by [5], [7].

Overlap of [1] abc=1 with [4] cbca=c:

Critical pair: abc=bca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [6].

Overlap of [5] bca=1 with [3] aac=cbc:

Critical pair: bccbc=ac.

Referenced by [7].

Overlap of [6] bccbc=ac with [4] cbca=c:

Critical pair: bcc=aca.

Defines rule #3.