Certificate for #5542 ⟨a, b | aaabaa=abaab⟩

Completion settings:

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

Axiom: aaabaa=abaab.

Flip LHS and RHS.

Referenced by [3].

Axiom: ab=c.

Defines rule #4.

Referenced by [3], [4], [5].

Simplify [1] abaab=aaabaa.

Reduce RHS:

Referenced by [4].

Overlap of [3] abaab=aacaa with [2] ab=c:

Critical pair: caab=aacaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.

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

Overlap of [4] aacaa=cac with [2] ab=c:

Critical pair: aacac=cacb.

Flip LHS and RHS.

Defines rule #5.

Overlap of [4] aacaa=cac with [4] aacaa=cac:

Critical pair: aaccac=caccaa.

Flip LHS and RHS.

Defines rule #2.

Overlap of [4] aacaa=cac with [4] aacaa=cac:

Critical pair: aacacac=cacacaa.

Flip LHS and RHS.

Defines rule #3.