Certificate for #1289 ⟨a, b | aaaaaabbba=1⟩

Completion settings:

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

Axiom: aaaaaabbba=1.

Referenced by [4].

Axiom: aaaaaaa=c.

Defines rule #8.

Referenced by [6], [7], [12], [13], [14].

Axiom: bbb=d.

Defines rule #7.

Referenced by [4], [5].

Overlap of [1] aaaaaabbba=1 with [3] bbb=d:

Critical pair: aaaaaada=1.

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

Overlap of [3] bbb=d with [3] bbb=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.

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].

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

Critical pair: cd=aaaaaada.

Reduce RHS:

Defines rule #3.

Referenced by [10], [12], [13], [14].

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

Critical pair: cbd=b.

Referenced by [15].

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

Critical pair: aaaaadaaaaaad=aaaaaadaaaada.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [12], [14].

Overlap of [11] aaada=aaaad with [11] aaada=aaaad:

Critical pair: aaadaaaad=aaaadaada.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [13].

Overlap of [2] aaaaaaa=c with [12] aaaaaadda=d:

Critical pair: ad=cdda.

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [14].

Overlap of [13] da=ad with [2] aaaaaaa=c:

Critical pair: dc=adaaaaaa.

Reduce RHS:

Defines rule #6.

Referenced by [15].

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

Critical pair: cb=bc.

Defines rule #2.