Certificate for #2199 ⟨a, b, c | aabc=1, acba=1⟩

Completion settings:

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

Axiom: aabc=1.

Referenced by [4].

Axiom: acba=1.

Referenced by [5], [6], [7], [10].

Axiom: bc=d.

Defines rule #3.

Referenced by [4], [8], [9].

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

Critical pair: aad=1.

Referenced by [5].

Overlap of [2] acba=1 with [4] aad=1:

Critical pair: acb=ad.

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

Overlap of [2] acba=1 with [5] acb=ad:

Critical pair: ada=1.

Referenced by [7], [10], [11].

Overlap of [2] acba=1 with [5] acb=ad:

Critical pair: acbad=cb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [8], [9].

Overlap of [3] bc=d with [7] cb=d:

Critical pair: bd=db.

Defines rule #2.

Referenced by [12].

Overlap of [7] cb=d with [3] bc=d:

Critical pair: cd=dc.

Defines rule #4.

Referenced by [13].

Overlap of [2] acba=1 with [6] ada=1:

Critical pair: acb=da.

Reduce LHS:

Defines rule #1.

Referenced by [11], [14], [15], [16], [17].

Overlap of [6] ada=1 with [10] ad=da:

Critical pair: daa=1.

Defines rule #6.

Referenced by [12], [13], [16], [17].

Overlap of [8] bd=db with [11] daa=1:

Critical pair: b=dbaa.

Flip LHS and RHS.

Referenced by [14].

Overlap of [9] cd=dc with [11] daa=1:

Critical pair: c=dcaa.

Flip LHS and RHS.

Referenced by [15].

Overlap of [10] ad=da with [12] dbaa=b:

Critical pair: ab=dabaa.

Flip LHS and RHS.

Referenced by [16].

Overlap of [10] ad=da with [13] dcaa=c:

Critical pair: ac=dacaa.

Flip LHS and RHS.

Referenced by [17].

Overlap of [10] ad=da with [14] dabaa=ab:

Critical pair: aab=daabaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #7.

Overlap of [10] ad=da with [15] dacaa=ac:

Critical pair: aac=daacaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #8.