Certificate for #1810 ⟨a, b, c | aba=ab, acc=1⟩

Completion settings:

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

Axiom: aba=ab.

Referenced by [4].

Axiom: acc=1.

Defines rule #4.

Referenced by [7].

Axiom: ab=d.

Defines rule #1.

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

Simplify [1] aba=ab.

Reduce RHS:

Referenced by [5].

Overlap of [4] aba=d with [3] ab=d:

Critical pair: da=d.

Defines rule #2.

Referenced by [6], [7].

Overlap of [5] da=d with [3] ab=d:

Critical pair: dd=db.

Flip LHS and RHS.

Defines rule #3.

Overlap of [5] da=d with [2] acc=1:

Critical pair: d=dcc.

Flip LHS and RHS.

Defines rule #5.