Certificate for #5957 ⟨a, b, c | ab=a, cbc=ca⟩

Completion settings:

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

Axiom: ab=a.

Defines rule #1.

Referenced by [5].

Axiom: cbc=ca.

Referenced by [4].

Axiom: ca=d.

Defines rule #3.

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

Simplify [2] cbc=ca.

Reduce RHS:

Defines rule #4.

Referenced by [6], [7].

Overlap of [3] ca=d with [1] ab=a:

Critical pair: ca=db.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [6].

Overlap of [4] cbc=d with [4] cbc=d:

Critical pair: cbd=dbc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

Overlap of [4] cbc=d with [3] ca=d:

Critical pair: cbd=da.

Flip LHS and RHS.

Defines rule #5.