Certificate for #4593 ⟨a, b | aabaaaab=baa⟩

Completion settings:

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

Axiom: aabaaaab=baa.

Referenced by [3].

Axiom: baaaa=c.

Referenced by [3], [4].

Overlap of [1] aabaaaab=baa with [2] baaaa=c:

Critical pair: aacb=baa.

Flip LHS and RHS.

Defines rule #4.

Referenced by [4], [5], [6], [7], [8], [9].

Overlap of [2] baaaa=c with [3] baa=aacb:

Critical pair: aacbaa=c.

Reduce LHS:

Defines rule #2.

Referenced by [5], [6], [7], [10], [11].

Overlap of [3] baa=aacb with [4] aacaacb=c:

Critical pair: bc=aacbcaacb.

Flip LHS and RHS.

Referenced by [10].

Overlap of [3] baa=aacb with [4] aacaacb=c:

Critical pair: bac=aacbacaacb.

Flip LHS and RHS.

Referenced by [11].

Overlap of [4] aacaacb=c with [3] baa=aacb:

Critical pair: aacaacaacb=caa.

Reduce LHS:

Defines rule #1.

Referenced by [8], [9].

Overlap of [3] baa=aacb with [7] aacc=caa:

Critical pair: bcaa=aacbcc.

Referenced by [10].

Overlap of [3] baa=aacb with [7] aacc=caa:

Critical pair: bacaa=aacbacc.

Referenced by [11].

Simplify [5] aacbcaacb=bc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

Simplify [6] aacbacaacb=bac.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.