Certificate for #6436 ⟨a, b | aab=b, bbabb=a⟩

Completion settings:

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

Axiom: aab=b.

Defines rule #7.

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

Axiom: bbabb=a.

Referenced by [4].

Axiom: bab=c.

Defines rule #9.

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

Overlap of [2] bbabb=a with [3] bab=c:

Critical pair: bcb=a.

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

Overlap of [1] aab=b with [3] bab=c:

Critical pair: aac=bab.

Reduce RHS:

Defines rule #3.

Referenced by [11], [12], [14].

Overlap of [3] bab=c with [3] bab=c:

Critical pair: bac=cab.

Flip LHS and RHS.

Defines rule #8.

Overlap of [1] aab=b with [4] bcb=a:

Critical pair: aaa=bcb.

Reduce RHS:

Defines rule #2.

Overlap of [4] bcb=a with [3] bab=c:

Critical pair: bcc=aab.

Reduce RHS:

Referenced by [10], [13].

Overlap of [4] bcb=a with [4] bcb=a:

Critical pair: bca=acb.

Flip LHS and RHS.

Referenced by [14].

Overlap of [4] bcb=a with [8] bcc=b:

Critical pair: bcb=acc.

Reduce LHS:

Flip LHS and RHS.

Referenced by [11].

Overlap of [5] aac=c with [10] acc=a:

Critical pair: aa=cc.

Flip LHS and RHS.

Defines rule #1.

Referenced by [12].

Overlap of [11] cc=aa with [11] cc=aa:

Critical pair: caa=aac.

Reduce RHS:

Defines rule #4.

Referenced by [13].

Overlap of [8] bcc=b with [12] caa=c:

Critical pair: bcc=baa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Overlap of [5] aac=c with [9] acb=bca:

Critical pair: abca=cb.

Flip LHS and RHS.

Defines rule #6.