Certificate for #7051 ⟨a, b, c | ab=1, bcaca=c⟩

Completion settings:

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

Axiom: ab=1.

Defines rule #7.

Referenced by [5], [6], [8].

Axiom: bcaca=c.

Referenced by [4].

Axiom: ac=d.

Defines rule #6.

Referenced by [4], [5], [7], [9].

Overlap of [2] bcaca=c with [3] ac=d:

Critical pair: bcda=c.

Referenced by [5], [6], [10].

Overlap of [1] ab=1 with [4] bcda=c:

Critical pair: ac=cda.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [7], [8], [9], [10].

Overlap of [4] bcda=c with [1] ab=1:

Critical pair: bcd=cb.

Flip LHS and RHS.

Defines rule #8.

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

Critical pair: ad=dda.

Defines rule #1.

Overlap of [5] cda=d with [1] ab=1:

Critical pair: cd=db.

Flip LHS and RHS.

Defines rule #3.

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

Critical pair: cdd=dc.

Defines rule #2.

Overlap of [4] bcda=c with [5] cda=d:

Critical pair: bd=c.

Defines rule #4.