Certificate for #2295 ⟨a, b | abaaaab=baa⟩

Completion settings:

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

Axiom: abaaaab=baa.

Referenced by [3].

Axiom: abaa=c.

Referenced by [3], [4], [5], [6], [8], [9].

Overlap of [1] abaaaab=baa with [2] abaa=c:

Critical pair: caab=baa.

Referenced by [5], [7].

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

Critical pair: abac=cbaa.

Flip LHS and RHS.

Referenced by [10].

Overlap of [3] caab=baa with [2] abaa=c:

Critical pair: cac=baaaa.

Flip LHS and RHS.

Referenced by [6].

Overlap of [2] abaa=c with [5] baaaa=cac:

Critical pair: acac=caa.

Flip LHS and RHS.

Defines rule #3.

Referenced by [7].

Overlap of [3] caab=baa with [6] caa=acac:

Critical pair: acacb=baa.

Flip LHS and RHS.

Defines rule #2.

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

Overlap of [7] baa=acacb with [2] abaa=c:

Critical pair: bac=acacbbaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #7.

Overlap of [2] abaa=c with [7] baa=acacb:

Critical pair: aacacb=c.

Defines rule #5.

Referenced by [11], [12].

Overlap of [4] cbaa=abac with [7] baa=acacb:

Critical pair: cacacb=abac.

Defines rule #4.

Overlap of [7] baa=acacb with [9] aacacb=c:

Critical pair: bc=acacbcacb.

Flip LHS and RHS.

Defines rule #6.

Referenced by [12].

Overlap of [9] aacacb=c with [11] acacbcacb=bc:

Critical pair: abc=ccacb.

Flip LHS and RHS.

Defines rule #1.