Certificate for #7602 ⟨a, b, c | ab=1, cbac=bc⟩

Completion settings:

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

Axiom: ab=1.

Defines rule #6.

Referenced by [5], [14].

Axiom: cbac=bc.

Referenced by [4].

Axiom: bc=d.

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

Simplify [2] cbac=bc.

Reduce RHS:

Referenced by [6].

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

Critical pair: ad=c.

Flip LHS and RHS.

Defines rule #3.

Referenced by [6], [9].

Simplify [4] cbac=d.

Reduce LHS:

Referenced by [7], [8], [12].

Overlap of [6] adbaad=d with [6] adbaad=d:

Critical pair: adbad=dbaad.

Referenced by [8], [10].

Overlap of [7] adbad=dbaad with [6] adbaad=d:

Critical pair: adbd=dbaadbaad.

Reduce RHS:

Referenced by [11].

Overlap of [3] bc=d with [5] c=ad:

Critical pair: bad=d.

Defines rule #5.

Referenced by [10], [11], [12], [13].

Overlap of [7] adbad=dbaad with [9] bad=d:

Critical pair: add=dbaad.

Flip LHS and RHS.

Defines rule #7.

Referenced by [12].

Simplify [8] adbd=dbad.

Reduce RHS:

Referenced by [13].

Overlap of [9] bad=d with [6] adbaad=d:

Critical pair: bd=dbaad.

Reduce RHS:

Defines rule #4.

Referenced by [13], [14].

Overlap of [9] bad=d with [11] adbd=dd:

Critical pair: bdd=dbd.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [1] ab=1 with [12] bd=add:

Critical pair: aadd=d.

Defines rule #1.