Certificate for #1532 ⟨a, b, c | ab=1, cac=ac⟩

Completion settings:

• Auxiliary generators:
  1. d = ca
• 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 #2.

Referenced by [5].

Axiom: cac=ac.

Referenced by [4].

Axiom: ca=d.

Referenced by [4], [5], [6], [9].

Overlap of [2] cac=ac with [3] ca=d:

Critical pair: dc=ac.

Flip LHS and RHS.

Referenced by [7].

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

Critical pair: c=db.

Defines rule #5.

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

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

Critical pair: dba=d.

Defines rule #4.

Referenced by [8].

Simplify [4] ac=dc.

Reduce LHS:

Reduce RHS:

Referenced by [8].

Overlap of [7] adb=ddb with [6] dba=d:

Critical pair: ad=ddba.

Reduce RHS:

Defines rule #3.

Referenced by [9].

Overlap of [3] ca=d with [8] ad=dd:

Critical pair: cdd=dd.

Reduce LHS:

Defines rule #1.