Certificate for #3188 ⟨a, b, c | ba=ab, abcc=1⟩

Completion settings:

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

Axiom: ba=ab.

Referenced by [4].

Axiom: abcc=1.

Referenced by [5].

Axiom: ab=d.

Defines rule #1.

Referenced by [4], [5], [6], [7].

Simplify [1] ba=ab.

Reduce RHS:

Defines rule #2.

Referenced by [6], [7].

Overlap of [2] abcc=1 with [3] ab=d:

Critical pair: dcc=1.

Defines rule #5.

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

Critical pair: bd=db.

Flip LHS and RHS.

Defines rule #4.

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

Critical pair: ad=da.

Flip LHS and RHS.

Defines rule #3.