Certificate for #4411 ⟨a, b | aaaaabba=baa⟩

Completion settings:

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

Axiom: aaaaabba=baa.

Referenced by [4].

Axiom: bb=c.

Defines rule #10.

Referenced by [4], [5], [6], [8].

Axiom: caa=d.

Defines rule #4.

Referenced by [6], [7], [8], [9], [10], [11].

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

Critical pair: aaaaaca=baa.

Flip LHS and RHS.

Defines rule #7.

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

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

Critical pair: bc=cb.

Flip LHS and RHS.

Defines rule #9.

Referenced by [7].

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

Critical pair: baaaaaca=caa.

Reduce LHS:

Reduce RHS:

Defines rule #2.

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

Overlap of [5] cb=bc with [4] baa=aaaaaca:

Critical pair: caaaaaca=bcaa.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [8].

Overlap of [2] bb=c with [7] bd=daaaca:

Critical pair: bdaaaca=cd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Overlap of [3] caa=d with [6] aaaaadaaca=d:

Critical pair: cad=daaaadaaca.

Defines rule #5.

Overlap of [4] baa=aaaaaca with [6] aaaaadaaca=d:

Critical pair: bad=aaaaacaaaaadaaca.

Reduce RHS:

Defines rule #8.

Overlap of [6] aaaaadaaca=d with [3] caa=d:

Critical pair: aaaaadaad=da.

Defines rule #1.