Certificate for #7013 ⟨a, b, c | ab=1, bbaca=c⟩

Completion settings:

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

Axiom: ab=1.

Defines rule #7.

Referenced by [4], [5].

Axiom: bbaca=c.

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

Axiom: cb=d.

Defines rule #2.

Referenced by [4], [7], [8].

Overlap of [2] bbaca=c with [1] ab=1:

Critical pair: bbac=cb.

Reduce RHS:

Referenced by [5], [6], [7], [9], [10].

Overlap of [1] ab=1 with [4] bbac=d:

Critical pair: ad=bac.

Flip LHS and RHS.

Referenced by [8], [10], [12].

Overlap of [2] bbaca=c with [4] bbac=d:

Critical pair: da=c.

Defines rule #8.

Referenced by [8], [12], [13].

Overlap of [4] bbac=d with [3] cb=d:

Critical pair: bbad=db.

Referenced by [11].

Overlap of [3] cb=d with [5] bac=ad:

Critical pair: cad=dac.

Reduce RHS:

Referenced by [9].

Overlap of [2] bbaca=c with [8] cad=cc:

Critical pair: bbacc=cd.

Reduce LHS:

Defines rule #1.

Overlap of [4] bbac=d with [5] bac=ad:

Critical pair: bad=d.

Referenced by [11], [12], [14].

Overlap of [7] bbad=db with [10] bad=d:

Critical pair: bd=db.

Flip LHS and RHS.

Defines rule #6.

Overlap of [10] bad=d with [6] da=c:

Critical pair: bac=da.

Reduce LHS:

Reduce RHS:

Defines rule #5.

Referenced by [13], [14].

Overlap of [12] ad=c with [6] da=c:

Critical pair: ac=ca.

Defines rule #4.

Overlap of [10] bad=d with [12] ad=c:

Critical pair: bc=d.

Defines rule #3.