Certificate for #7557 ⟨a, b, c | ab=1, bcbc=cb⟩

Completion settings:

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

Axiom: ab=1.

Defines rule #5.

Referenced by [6].

Axiom: bcbc=cb.

Referenced by [4].

Axiom: cb=d.

Defines rule #3.

Referenced by [4], [5], [7], [8].

Simplify [2] bcbc=cb.

Reduce RHS:

Referenced by [5].

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

Critical pair: bdc=d.

Defines rule #2.

Referenced by [6], [7], [8].

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

Critical pair: ad=dc.

Defines rule #6.

Overlap of [3] cb=d with [5] bdc=d:

Critical pair: cd=ddc.

Defines rule #4.

Overlap of [5] bdc=d with [3] cb=d:

Critical pair: bdd=db.

Defines rule #1.