Certificate for #4631 ⟨a, b | aabaabba=baa⟩

Completion settings:

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

Axiom: aabaabba=baa.

Referenced by [4].

Axiom: bb=c.

Defines rule #11.

Referenced by [4], [6], [7], [10].

Axiom: abaac=d.

Referenced by [4], [5].

Overlap of [1] aabaabba=baa with [2] bb=c:

Critical pair: aabaaca=baa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [5], [7], [8], [9].

Overlap of [3] abaac=d with [4] baa=ada:

Critical pair: aadac=d.

Defines rule #3.

Referenced by [8], [9], [11], [13], [14].

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

Critical pair: bc=cb.

Defines rule #10.

Overlap of [2] bb=c with [4] baa=ada:

Critical pair: bada=caa.

Referenced by [12].

Overlap of [4] baa=ada with [5] aadac=d:

Critical pair: bd=adadac.

Defines rule #7.

Overlap of [4] baa=ada with [5] aadac=d:

Critical pair: bad=adaadac.

Reduce RHS:

Defines rule #9.

Referenced by [10], [12].

Overlap of [2] bb=c with [9] bad=add:

Critical pair: badd=cad.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [11].

Overlap of [5] aadac=d with [10] cad=addd:

Critical pair: aadaaddd=dad.

Defines rule #2.

Simplify [7] bada=caa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [13], [14].

Overlap of [5] aadac=d with [12] caa=adda:

Critical pair: aadaadda=daa.

Defines rule #1.

Overlap of [12] caa=adda with [5] aadac=d:

Critical pair: cd=addadac.

Defines rule #4.