Certificate for #5708 ⟨a, b, c | aa=b, acb=cb⟩

Completion settings:

• Auxiliary generators:
  1. d = cb
• Reduction order:
  • Left-to-right shortlex with b < a < d < c

Axiom: aa=b.

Defines rule #3.

Referenced by [6], [7].

Axiom: acb=cb.

Referenced by [4].

Axiom: cb=d.

Defines rule #5.

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

Simplify [2] acb=cb.

Reduce RHS:

Referenced by [5].

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

Critical pair: ad=d.

Defines rule #4.

Referenced by [7].

Overlap of [1] aa=b with [1] aa=b:

Critical pair: ab=ba.

Defines rule #2.

Overlap of [1] aa=b with [5] ad=d:

Critical pair: ad=bd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [8].

Overlap of [3] cb=d with [7] bd=d:

Critical pair: cd=dd.

Defines rule #6.