Certificate for #5567 ⟨a, b, c | ab=c, baca=c⟩

Completion settings:

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

Axiom: ab=c.

Defines rule #8.

Referenced by [5], [6], [9].

Axiom: baca=c.

Referenced by [4].

Axiom: ac=d.

Defines rule #7.

Referenced by [4], [5], [7], [8], [10].

Overlap of [2] baca=c with [3] ac=d:

Critical pair: bda=c.

Defines rule #6.

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

Overlap of [1] ab=c with [4] bda=c:

Critical pair: ac=cda.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [8], [9], [10].

Overlap of [4] bda=c with [1] ab=c:

Critical pair: bdc=cb.

Defines rule #2.

Overlap of [4] bda=c with [3] ac=d:

Critical pair: bdd=cc.

Defines rule #4.

Overlap of [3] ac=d with [5] cda=d:

Critical pair: ad=dda.

Defines rule #9.

Overlap of [5] cda=d with [1] ab=c:

Critical pair: cdc=db.

Defines rule #1.

Overlap of [5] cda=d with [3] ac=d:

Critical pair: cdd=dc.

Defines rule #3.