Certificate for #4807 ⟨a, b | abaabbba=baa⟩

Completion settings:

• Reduction order:
  • Right-to-left recursive path with deg(a) = deg(c) = 0, a < c; deg(d) = 1; deg(b) = 2
• Auxiliary generators:
  1. baabbb=c
  2. bbb=d

Axiom: abaabbba=baa.

Referenced by [4].

Axiom: baabbb=c.

Referenced by [4], [5].

Axiom: bbb=d.

Defines rule #11.

Referenced by [5], [6], [7], [9], [11].

Overlap of [1] abaabbba=baa with [2] baabbb=c:

Critical pair: aca=baa.

Flip LHS and RHS.

Defines rule #8.

Referenced by [5], [7], [8].

Overlap of [2] baabbb=c with [4] baa=aca:

Critical pair: acabbb=c.

Reduce LHS:

Defines rule #3.

Referenced by [8], [10], [12], [14].

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

Critical pair: bd=db.

Defines rule #10.

Overlap of [3] bbb=d with [4] baa=aca:

Critical pair: bbaca=daa.

Referenced by [13].

Overlap of [4] baa=aca with [5] acad=c:

Critical pair: bac=acacad.

Reduce RHS:

Defines rule #9.

Referenced by [9], [10], [11], [13].

Overlap of [3] bbb=d with [8] bac=acc:

Critical pair: bbacc=dac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [12].

Overlap of [8] bac=acc with [5] acad=c:

Critical pair: bc=accad.

Defines rule #7.

Referenced by [11].

Overlap of [3] bbb=d with [10] bc=accad:

Critical pair: bbaccad=dc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Overlap of [5] acad=c with [9] dac=acccc:

Critical pair: acaacccc=cac.

Defines rule #2.

Simplify [7] bbaca=daa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [14].

Overlap of [5] acad=c with [13] daa=accca:

Critical pair: acaaccca=caa.

Defines rule #1.