Certificate for #477 ⟨a, b | ababba=ba⟩

Completion settings:

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

Axiom: ababba=ba.

Referenced by [3].

Axiom: ababb=c.

Referenced by [3], [4].

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

Critical pair: ca=ba.

Flip LHS and RHS.

Defines rule #1.

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

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

Critical pair: acabb=c.

Defines rule #3.

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

Overlap of [3] ba=ca with [4] acabb=c:

Critical pair: bc=cacabb.

Reduce RHS:

Defines rule #2.

Referenced by [6], [7].

Overlap of [4] acabb=c with [3] ba=ca:

Critical pair: acabca=ca.

Reduce LHS:

Defines rule #4.

Overlap of [4] acabb=c with [5] bc=cc:

Critical pair: acabcc=cc.

Reduce LHS:

Defines rule #5.