Certificate for #4260 ⟨a, b, c | aab=1, bcaa=c⟩

Completion settings:

• Auxiliary generators:
  1. d = cb
• Reduction order:
  • Left-to-right shortlex with c < b < a < d

Axiom: aab=1.

Defines rule #7.

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

Axiom: bcaa=c.

Referenced by [4], [5], [6], [8], [11].

Axiom: cb=d.

Defines rule #1.

Referenced by [5], [9], [10].

Overlap of [1] aab=1 with [2] bcaa=c:

Critical pair: aac=caa.

Defines rule #6.

Overlap of [2] bcaa=c with [1] aab=1:

Critical pair: bc=cb.

Reduce RHS:

Defines rule #2.

Referenced by [6], [7], [8], [9], [10], [11], [12].

Overlap of [2] bcaa=c with [1] aab=1:

Critical pair: bca=cab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [12].

Overlap of [1] aab=1 with [5] bc=d:

Critical pair: aad=c.

Defines rule #8.

Referenced by [11].

Overlap of [2] bcaa=c with [5] bc=d:

Critical pair: daa=c.

Defines rule #11.

Overlap of [3] cb=d with [5] bc=d:

Critical pair: cd=dc.

Flip LHS and RHS.

Defines rule #3.

Overlap of [5] bc=d with [3] cb=d:

Critical pair: bd=db.

Flip LHS and RHS.

Defines rule #4.

Overlap of [2] bcaa=c with [7] aad=c:

Critical pair: bcac=cad.

Reduce LHS:

Defines rule #9.

Overlap of [5] bc=d with [6] cab=da:

Critical pair: bda=dab.

Flip LHS and RHS.

Defines rule #10.