Certificate for #2583 ⟨a, b | abaaba=abab⟩

Completion settings:

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

Axiom: abaaba=abab.

Referenced by [3].

Axiom: abab=c.

Defines rule #6.

Referenced by [3], [4], [6], [7], [8].

Simplify [1] abaaba=abab.

Reduce RHS:

Defines rule #7.

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

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

Critical pair: abc=cab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [5].

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

Critical pair: abac=caba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [8].

Overlap of [3] abaaba=c with [2] abab=c:

Critical pair: abac=cb.

Flip LHS and RHS.

Defines rule #3.

Overlap of [2] abab=c with [3] abaaba=c:

Critical pair: abc=caaba.

Flip LHS and RHS.

Defines rule #5.

Overlap of [2] abab=c with [5] abca=abac:

Critical pair: ababac=cca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.