Certificate for #4058 ⟨a, b | aaabbbbba=ab⟩

Completion settings:

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

Axiom: aaabbbbba=ab.

Referenced by [3].

Axiom: bbbbba=c.

Defines rule #7.

Referenced by [3], [4], [5], [6].

Overlap of [1] aaabbbbba=ab with [2] bbbbba=c:

Critical pair: aaac=ab.

Flip LHS and RHS.

Defines rule #5.

Referenced by [4], [5].

Overlap of [2] bbbbba=c with [3] ab=aaac:

Critical pair: bbbbbaaac=cb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [5], [6].

Overlap of [3] ab=aaac with [2] bbbbba=c:

Critical pair: ac=aaacbbbba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [7].

Overlap of [4] cb=caac with [2] bbbbba=c:

Critical pair: cc=caacbbbba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [7], [8].

Overlap of [5] aaacaacaacaacaaca=ac with [6] caacaacaacaacaaca=cc:

Critical pair: aaacc=acaca.

Defines rule #1.

Overlap of [6] caacaacaacaacaaca=cc with [6] caacaacaacaacaaca=cc:

Critical pair: caacc=ccaca.

Defines rule #2.