Certificate for #4278 ⟨a, b, c | aab=1, bcca=c⟩

Completion settings:

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

Axiom: aab=1.

Defines rule #9.

Referenced by [5], [6].

Axiom: bcca=c.

Referenced by [4].

Axiom: bc=d.

Defines rule #5.

Referenced by [4], [5], [9], [11].

Overlap of [2] bcca=c with [3] bc=d:

Critical pair: dca=c.

Defines rule #4.

Referenced by [6], [7], [8], [10].

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

Critical pair: aad=c.

Defines rule #2.

Referenced by [7], [8].

Overlap of [4] dca=c with [1] aab=1:

Critical pair: dc=cab.

Flip LHS and RHS.

Defines rule #8.

Referenced by [9], [10].

Overlap of [4] dca=c with [5] aad=c:

Critical pair: dcc=cad.

Defines rule #3.

Overlap of [5] aad=c with [4] dca=c:

Critical pair: aac=cca.

Defines rule #1.

Overlap of [3] bc=d with [6] cab=dc:

Critical pair: bdc=dab.

Flip LHS and RHS.

Defines rule #10.

Overlap of [4] dca=c with [6] cab=dc:

Critical pair: ddc=cb.

Flip LHS and RHS.

Defines rule #6.

Referenced by [11].

Overlap of [3] bc=d with [10] cb=ddc:

Critical pair: bddc=db.

Flip LHS and RHS.

Defines rule #7.