Certificate for #16254 ⟨a, b | aab=ba, babb=ab⟩

Completion settings:

• Reduction order:
  • Left-to-right shortlex with a < b

Axiom: aab=ba.

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

Axiom: babb=ab.

Referenced by [3], [4], [5], [6].

Overlap of [1] aab=ba with [2] babb=ab:

Critical pair: aaab=baabb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [4].

Overlap of [3] bbab=aba with [2] babb=ab:

Critical pair: bab=abab.

Flip LHS and RHS.

Referenced by [5].

Overlap of [4] abab=bab with [2] babb=ab:

Critical pair: aab=babb.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Referenced by [6], [7].

Overlap of [2] babb=ab with [5] ba=ab:

Critical pair: abbb=ab.

Defines rule #3.

Simplify [1] aab=ba.

Reduce RHS:

Defines rule #2.