Certificate for #9749 ⟨a, b | aa=1, abbabbb=b⟩

Completion settings:

• Auxiliary generators:
  1. c = bab
• Reduction order:
  • Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1

Axiom: aa=1.

Defines rule #1.

Referenced by [6], [8], [12], [13].

Axiom: abbabbb=b.

Referenced by [4].

Axiom: bab=c.

Defines rule #7.

Referenced by [4], [5], [7], [9], [13].

Overlap of [2] abbabbb=b with [3] bab=c:

Critical pair: abcbb=b.

Referenced by [6], [7].

Overlap of [3] bab=c with [3] bab=c:

Critical pair: bac=cab.

Flip LHS and RHS.

Defines rule #6.

Overlap of [1] aa=1 with [4] abcbb=b:

Critical pair: ab=bcbb.

Flip LHS and RHS.

Referenced by [13].

Overlap of [4] abcbb=b with [3] bab=c:

Critical pair: abcbc=bab.

Reduce RHS:

Referenced by [8], [9], [10].

Overlap of [1] aa=1 with [7] abcbc=c:

Critical pair: ac=bcbc.

Flip LHS and RHS.

Referenced by [10], [11].

Overlap of [3] bab=c with [7] abcbc=c:

Critical pair: bc=ccbc.

Flip LHS and RHS.

Referenced by [11].

Overlap of [7] abcbc=c with [8] bcbc=ac:

Critical pair: abcac=cbc.

Flip LHS and RHS.

Referenced by [14].

Overlap of [9] ccbc=bc with [8] bcbc=ac:

Critical pair: ccac=bcbc.

Reduce RHS:

Defines rule #3.

Referenced by [12].

Overlap of [11] ccac=ac with [11] ccac=ac:

Critical pair: ccaac=accac.

Reduce LHS:

Reduce RHS:

Defines rule #2.

Overlap of [6] bcbb=ab with [6] bcbb=ab:

Critical pair: bcbab=abcbb.

Reduce LHS:

Reduce RHS:

Defines rule #4.

Referenced by [14].

Overlap of [10] cbc=abcac with [13] bcc=b:

Critical pair: cb=abcacc.

Defines rule #5.