Certificate for #7576 ⟨a, b, c | ab=1, caac=ac⟩

Completion settings:

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

Axiom: ab=1.

Defines rule #3.

Referenced by [5], [8].

Axiom: caac=ac.

Referenced by [4].

Axiom: caa=d.

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

Overlap of [2] caac=ac with [3] caa=d:

Critical pair: dc=ac.

Flip LHS and RHS.

Referenced by [6].

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

Critical pair: ca=db.

Referenced by [6], [7], [8], [9], [11].

Overlap of [4] ac=dc with [3] caa=d:

Critical pair: ad=dcaa.

Reduce RHS:

Flip LHS and RHS.

Referenced by [10].

Overlap of [3] caa=d with [5] ca=db:

Critical pair: dba=d.

Defines rule #5.

Referenced by [10], [12].

Overlap of [5] ca=db with [1] ab=1:

Critical pair: c=dbb.

Defines rule #7.

Referenced by [9], [11].

Overlap of [5] ca=db with [8] c=dbb:

Critical pair: dbba=db.

Defines rule #6.

Simplify [6] ddba=ad.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [11], [12].

Overlap of [5] ca=db with [10] ad=dd:

Critical pair: cdd=dbd.

Reduce LHS:

Defines rule #2.

Overlap of [7] dba=d with [10] ad=dd:

Critical pair: dbdd=dd.

Defines rule #1.