Certificate for #3004 ⟨a, b | aaabbbbbbba=1⟩

Completion settings:

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

Axiom: aaabbbbbbba=1.

Referenced by [4].

Axiom: aaaa=c.

Defines rule #7.

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

Axiom: bbbbbbb=d.

Defines rule #8.

Referenced by [4], [12].

Overlap of [1] aaabbbbbbba=1 with [3] bbbbbbb=d:

Critical pair: aaada=1.

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

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

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #1.

Overlap of [2] aaaa=c with [4] aaada=1:

Critical pair: a=cda.

Flip LHS and RHS.

Referenced by [8].

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

Critical pair: aaad=aada.

Flip LHS and RHS.

Referenced by [9], [10], [11].

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

Critical pair: cd=aaada.

Reduce RHS:

Defines rule #3.

Referenced by [13].

Overlap of [4] aaada=1 with [7] aada=aaad:

Critical pair: aaadaaad=ada.

Reduce LHS:

Flip LHS and RHS.

Referenced by [11].

Overlap of [7] aada=aaad with [7] aada=aaad:

Critical pair: aadaaad=aaadada.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [11].

Overlap of [10] da=ad with [2] aaaa=c:

Critical pair: dc=adaaa.

Reduce RHS:

Defines rule #6.

Referenced by [14].

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

Critical pair: bd=db.

Flip LHS and RHS.

Defines rule #5.

Referenced by [13].

Overlap of [8] cd=1 with [12] db=bd:

Critical pair: cbd=b.

Referenced by [14].

Overlap of [13] cbd=b with [11] dc=1:

Critical pair: cb=bc.

Defines rule #2.