Certificate for #2057 ⟨a, b | abababba=ab⟩

Completion settings:

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

Axiom: abababba=ab.

Referenced by [4].

Axiom: ab=c.

Defines rule #3.

Referenced by [4], [5], [6], [11].

Axiom: cb=d.

Defines rule #4.

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

Simplify [1] abababba=ab.

Reduce RHS:

Referenced by [5].

Overlap of [4] abababba=c with [2] ab=c:

Critical pair: cababba=c.

Reduce LHS:

Defines rule #1.

Referenced by [6], [8].

Overlap of [5] ccda=c with [2] ab=c:

Critical pair: ccdc=cb.

Reduce RHS:

Defines rule #2.

Referenced by [7], [8], [9], [10].

Overlap of [6] ccdc=d with [3] cb=d:

Critical pair: ccdd=db.

Flip LHS and RHS.

Defines rule #9.

Referenced by [11].

Overlap of [6] ccdc=d with [5] ccda=c:

Critical pair: ccdc=dcda.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [10].

Overlap of [6] ccdc=d with [6] ccdc=d:

Critical pair: ccdd=dcdc.

Flip LHS and RHS.

Defines rule #8.

Overlap of [6] ccdc=d with [8] dcda=d:

Critical pair: ccd=dda.

Flip LHS and RHS.

Defines rule #5.

Referenced by [11].

Overlap of [10] dda=ccd with [2] ab=c:

Critical pair: ddc=ccdb.

Reduce RHS:

Defines rule #7.