Certificate for #83 ⟨a, b, c | abc=1, cba=1⟩

Completion settings:

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

Axiom: abc=1.

Referenced by [4].

Axiom: cba=1.

Referenced by [5], [6], [7].

Axiom: bc=d.

Defines rule #5.

Referenced by [4], [6], [8], [9].

Overlap of [1] abc=1 with [3] bc=d:

Critical pair: ad=1.

Defines rule #1.

Referenced by [5], [11], [12].

Overlap of [2] cba=1 with [4] ad=1:

Critical pair: cb=d.

Defines rule #8.

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

Overlap of [3] bc=d with [2] cba=1:

Critical pair: b=dba.

Flip LHS and RHS.

Referenced by [11].

Overlap of [2] cba=1 with [5] cb=d:

Critical pair: da=1.

Defines rule #2.

Referenced by [10].

Overlap of [3] bc=d with [5] cb=d:

Critical pair: bd=db.

Defines rule #4.

Overlap of [5] cb=d with [3] bc=d:

Critical pair: cd=dc.

Defines rule #7.

Referenced by [10].

Overlap of [9] cd=dc with [7] da=1:

Critical pair: c=dca.

Flip LHS and RHS.

Referenced by [12].

Overlap of [4] ad=1 with [6] dba=b:

Critical pair: ab=ba.

Flip LHS and RHS.

Defines rule #3.

Overlap of [4] ad=1 with [10] dca=c:

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #6.