Certificate for #2898 ⟨a, b | aaaabbbbbba=1⟩

Completion settings:

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

Axiom: aaaabbbbbba=1.

Referenced by [4].

Axiom: aaaaa=c.

Defines rule #7.

Referenced by [5], [6], [11], [12], [14].

Axiom: bbbbbb=d.

Defines rule #8.

Referenced by [4], [9].

Overlap of [1] aaaabbbbbba=1 with [3] bbbbbb=d:

Critical pair: aaaada=1.

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

Overlap of [2] aaaaa=c with [2] aaaaa=c:

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #1.

Referenced by [16].

Overlap of [2] aaaaa=c with [4] aaaada=1:

Critical pair: a=cda.

Flip LHS and RHS.

Referenced by [8].

Overlap of [4] aaaada=1 with [4] aaaada=1:

Critical pair: aaaad=aaada.

Flip LHS and RHS.

Referenced by [11], [12].

Overlap of [6] cda=a with [4] aaaada=1:

Critical pair: cd=aaaada.

Reduce RHS:

Defines rule #3.

Referenced by [10], [11], [12], [14], [17].

Overlap of [3] bbbbbb=d with [3] bbbbbb=d:

Critical pair: bd=db.

Flip LHS and RHS.

Defines rule #5.

Referenced by [10].

Overlap of [8] cd=1 with [9] db=bd:

Critical pair: cbd=b.

Referenced by [15].

Overlap of [7] aaada=aaaad with [7] aaada=aaaad:

Critical pair: aaadaaaad=aaaadaada.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [12], [13].

Overlap of [11] ada=aad with [2] aaaaa=c:

Critical pair: adc=aadaaaa.

Reduce RHS:

Referenced by [13].

Overlap of [11] ada=aad with [12] adc=a:

Critical pair: ada=aaddc.

Reduce LHS:

Flip LHS and RHS.

Referenced by [14].

Overlap of [2] aaaaa=c with [13] aaddc=aad:

Critical pair: aaaaad=cddc.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [15], [16].

Overlap of [10] cbd=b with [14] dc=1:

Critical pair: cb=bc.

Defines rule #2.

Overlap of [14] dc=1 with [5] ca=ac:

Critical pair: dac=a.

Referenced by [17].

Overlap of [16] dac=a with [8] cd=1:

Critical pair: da=ad.

Defines rule #4.