Certificate for #2604 ⟨a, b | ababba=abab⟩

Completion settings:

• Auxiliary generators:
  1. c = ababb
• Reduction order:
  • Left-to-right shortlex with a < c < b

Axiom: ababba=abab.

Referenced by [3].

Axiom: ababb=c.

Referenced by [3], [4].

Overlap of [1] ababba=abab with [2] ababb=c:

Critical pair: ca=abab.

Flip LHS and RHS.

Defines rule #4.

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

Overlap of [2] ababb=c with [3] abab=ca:

Critical pair: cab=c.

Defines rule #2.

Referenced by [6], [7].

Overlap of [3] abab=ca with [3] abab=ca:

Critical pair: abca=caab.

Flip LHS and RHS.

Defines rule #5.

Overlap of [4] cab=c with [3] abab=ca:

Critical pair: cca=cab.

Reduce RHS:

Defines rule #3.

Referenced by [7].

Overlap of [6] cca=c with [4] cab=c:

Critical pair: cc=cb.

Flip LHS and RHS.

Defines rule #1.