Certificate for #7609 ⟨a, b, c | ab=1, cbcc=bc⟩

Completion settings:

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

Axiom: ab=1.

Defines rule #6.

Referenced by [6].

Axiom: cbcc=bc.

Referenced by [4].

Axiom: bc=d.

Referenced by [4], [5], [6], [9].

Simplify [2] cbcc=bc.

Reduce RHS:

Referenced by [5].

Overlap of [4] cbcc=d with [3] bc=d:

Critical pair: cdc=d.

Referenced by [7].

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

Critical pair: ad=c.

Flip LHS and RHS.

Defines rule #3.

Referenced by [7], [9].

Simplify [5] cdc=d.

Reduce LHS:

Defines rule #2.

Referenced by [8], [10].

Overlap of [7] addad=d with [7] addad=d:

Critical pair: addd=ddad.

Defines rule #1.

Overlap of [3] bc=d with [6] c=ad:

Critical pair: bad=d.

Defines rule #5.

Referenced by [10].

Overlap of [9] bad=d with [7] addad=d:

Critical pair: bd=ddad.

Defines rule #4.