Certificate for #7413 ⟨a, b, c | ab=1, acac=ca⟩

Completion settings:

• Auxiliary generators:
  1. d = ca
• Reduction order:
  • Left-to-right recursive path with deg(d) = 0; deg(a) = 1; deg(c) = 2; deg(b) = 3

Axiom: ab=1.

Defines rule #6.

Referenced by [6].

Axiom: acac=ca.

Referenced by [4].

Axiom: ca=d.

Defines rule #2.

Referenced by [4], [5], [6], [7], [8].

Simplify [2] acac=ca.

Reduce RHS:

Referenced by [5].

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

Critical pair: adc=d.

Defines rule #4.

Referenced by [7], [8].

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

Critical pair: c=db.

Flip LHS and RHS.

Defines rule #5.

Overlap of [3] ca=d with [5] adc=d:

Critical pair: cd=ddc.

Flip LHS and RHS.

Defines rule #3.

Overlap of [5] adc=d with [3] ca=d:

Critical pair: add=da.

Flip LHS and RHS.

Defines rule #1.