Certificate for #7847 ⟨a, b, c | ab=1, cba=bac⟩

Completion settings:

• Auxiliary generators:
  1. d = ac
• Reduction order:
  • Left-to-right recursive path with deg(a) = deg(b) = deg(d) = 0, a < b < d; deg(c) = 1

Axiom: ab=1.

Defines rule #1.

Referenced by [5], [6].

Axiom: cba=bac.

Flip LHS and RHS.

Referenced by [4].

Axiom: ac=d.

Defines rule #4.

Referenced by [4], [5], [7].

Overlap of [2] bac=cba with [3] ac=d:

Critical pair: bd=cba.

Flip LHS and RHS.

Referenced by [5], [6].

Overlap of [3] ac=d with [4] cba=bd:

Critical pair: abd=dba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [7].

Overlap of [4] cba=bd with [1] ab=1:

Critical pair: cb=bdb.

Defines rule #3.

Overlap of [5] dba=d with [3] ac=d:

Critical pair: dbd=dc.

Flip LHS and RHS.

Defines rule #5.