Certificate for #4532 ⟨a, b, c | abc=1, acaa=c⟩

Completion settings:

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

Axiom: abc=1.

Referenced by [4].

Axiom: acaa=c.

Referenced by [5], [6].

Axiom: bc=d.

Defines rule #4.

Referenced by [4], [8].

Overlap of [1] abc=1 with [3] bc=d:

Critical pair: ad=1.

Defines rule #1.

Referenced by [5], [7], [9].

Overlap of [2] acaa=c with [4] ad=1:

Critical pair: aca=cd.

Referenced by [6], [7], [10].

Overlap of [2] acaa=c with [5] aca=cd:

Critical pair: cda=c.

Referenced by [8], [11].

Overlap of [5] aca=cd with [4] ad=1:

Critical pair: ac=cdd.

Defines rule #3.

Overlap of [3] bc=d with [6] cda=c:

Critical pair: bc=dda.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [4] ad=1 with [8] dda=d:

Critical pair: ad=da.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [10].

Overlap of [9] da=1 with [5] aca=cd:

Critical pair: dcd=ca.

Referenced by [11].

Overlap of [10] dcd=ca with [6] cda=c:

Critical pair: dc=caa.

Defines rule #5.