Certificate for #30 ⟨a, b | aabba=1⟩

Completion settings:

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

Axiom: aabba=1.

Referenced by [4].

Axiom: aaa=c.

Defines rule #8.

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

Axiom: bb=d.

Defines rule #1.

Referenced by [4], [5].

Overlap of [1] aabba=1 with [3] bb=d:

Critical pair: aada=1.

Referenced by [7], [8], [9], [11], [12].

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

Critical pair: bd=db.

Flip LHS and RHS.

Defines rule #6.

Referenced by [10].

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

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #2.

Overlap of [2] aaa=c with [4] aada=1:

Critical pair: a=cda.

Flip LHS and RHS.

Referenced by [9].

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

Critical pair: aad=ada.

Flip LHS and RHS.

Referenced by [11], [12].

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

Critical pair: cd=aada.

Reduce RHS:

Defines rule #4.

Referenced by [10].

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

Critical pair: cbd=b.

Referenced by [13].

Overlap of [4] aada=1 with [8] ada=aad:

Critical pair: aadaad=da.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [12].

Overlap of [11] da=ad with [2] aaa=c:

Critical pair: dc=adaa.

Reduce RHS:

Defines rule #7.

Referenced by [13].

Overlap of [10] cbd=b with [12] dc=1:

Critical pair: cb=bc.

Defines rule #3.