Certificate for #5653 ⟨a, b | aabaab=abaaa⟩

Completion settings:

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

Axiom: aabaab=abaaa.

Flip LHS and RHS.

Referenced by [2], [3].

Axiom: abaaa=c.

Reduce LHS:

Defines rule #6.

Referenced by [3], [5], [6], [7], [8].

Simplify [1] abaaa=aabaab.

Reduce RHS:

Defines rule #7.

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

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

Critical pair: abaac=cbaaa.

Flip LHS and RHS.

Defines rule #5.

Overlap of [3] abaaa=c with [2] aabaab=c:

Critical pair: abac=cbaab.

Flip LHS and RHS.

Defines rule #2.

Overlap of [3] abaaa=c with [2] aabaab=c:

Critical pair: abaac=cabaab.

Flip LHS and RHS.

Defines rule #4.

Overlap of [2] aabaab=c with [3] abaaa=c:

Critical pair: aabac=caaa.

Flip LHS and RHS.

Defines rule #3.

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

Critical pair: aabc=caab.

Flip LHS and RHS.

Defines rule #1.