Certificate for #7270 ⟨a, b, c | aa=1, bcbc=cb⟩

Completion settings:

• Auxiliary generators:
  1. d = bc
• Reduction order:
  • Left-to-right recursive path with deg(a) = deg(d) = 0, a < d; deg(b) = 1; deg(c) = 2

Axiom: aa=1.

Defines rule #1.

Axiom: bcbc=cb.

Referenced by [4].

Axiom: bc=d.

Defines rule #5.

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

Overlap of [2] bcbc=cb with [3] bc=d:

Critical pair: dbc=cb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [5], [6].

Overlap of [3] bc=d with [4] cb=dd:

Critical pair: bdd=db.

Flip LHS and RHS.

Defines rule #2.

Overlap of [4] cb=dd with [3] bc=d:

Critical pair: cd=ddc.

Flip LHS and RHS.

Defines rule #4.