Certificate for #2807 ⟨a, b | aaaaaabbbba=1⟩

Completion settings:

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

Axiom: aaaaaabbbba=1.

Referenced by [4].

Axiom: aaaaaaa=c.

Defines rule #8.

Referenced by [6], [7], [11], [12], [13], [15].

Axiom: bbbb=d.

Defines rule #7.

Referenced by [4], [5].

Overlap of [1] aaaaaabbbba=1 with [3] bbbb=d:

Critical pair: aaaaaada=1.

Referenced by [7], [8], [9].

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

Critical pair: bd=db.

Flip LHS and RHS.

Defines rule #5.

Referenced by [10].

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

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #1.

Referenced by [17].

Overlap of [2] aaaaaaa=c with [4] aaaaaada=1:

Critical pair: a=cda.

Flip LHS and RHS.

Referenced by [9].

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

Critical pair: aaaaaad=aaaaada.

Flip LHS and RHS.

Referenced by [11], [12], [13].

Overlap of [7] cda=a with [4] aaaaaada=1:

Critical pair: cd=aaaaaada.

Reduce RHS:

Defines rule #3.

Referenced by [10], [11], [12], [13], [15], [18].

Overlap of [9] cd=1 with [5] db=bd:

Critical pair: cbd=b.

Referenced by [16].

Overlap of [8] aaaaada=aaaaaad with [8] aaaaada=aaaaaad:

Critical pair: aaaaadaaaaaad=aaaaaadaaaada.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [12], [13].

Overlap of [11] aaada=aaaad with [8] aaaaada=aaaaaad:

Critical pair: aaadaaaaaad=aaaadaaaada.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [13], [14].

Overlap of [12] ada=aad with [2] aaaaaaa=c:

Critical pair: adc=aadaaaaaa.

Reduce RHS:

Referenced by [14].

Overlap of [12] ada=aad with [13] adc=a:

Critical pair: ada=aaddc.

Reduce LHS:

Flip LHS and RHS.

Referenced by [15].

Overlap of [2] aaaaaaa=c with [14] aaddc=aad:

Critical pair: aaaaaaad=cddc.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [16], [17].

Overlap of [10] cbd=b with [15] dc=1:

Critical pair: cb=bc.

Defines rule #2.

Overlap of [15] dc=1 with [6] ca=ac:

Critical pair: dac=a.

Referenced by [18].

Overlap of [17] dac=a with [9] cd=1:

Critical pair: da=ad.

Defines rule #4.