Certificate for #1366 ⟨a, b, c | ab=1, bcca=c⟩

Completion settings:

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

Axiom: ab=1.

Defines rule #7.

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

Axiom: bcca=c.

Referenced by [4], [5], [9].

Axiom: ac=d.

Defines rule #2.

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

Overlap of [1] ab=1 with [2] bcca=c:

Critical pair: ac=cca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [6], [7], [8], [9].

Overlap of [2] bcca=c with [1] ab=1:

Critical pair: bcc=cb.

Flip LHS and RHS.

Defines rule #4.

Overlap of [3] ac=d with [4] cca=d:

Critical pair: ad=dca.

Defines rule #6.

Overlap of [4] cca=d with [1] ab=1:

Critical pair: cc=db.

Flip LHS and RHS.

Defines rule #5.

Overlap of [4] cca=d with [3] ac=d:

Critical pair: ccd=dc.

Defines rule #1.

Overlap of [2] bcca=c with [4] cca=d:

Critical pair: bd=c.

Defines rule #8.