Certificate for #19211 ⟨a, b | aba=b, abbbbb=b⟩

Completion settings:

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

Axiom: aba=b.

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

Axiom: abbbbb=b.

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

Overlap of [1] aba=b with [1] aba=b:

Critical pair: abb=bba.

Flip LHS and RHS.

Referenced by [4], [5].

Overlap of [2] abbbbb=b with [3] bba=abb:

Critical pair: abbbabb=ba.

Reduce LHS:

Referenced by [5], [6], [8].

Overlap of [2] abbbbb=b with [4] bbbbb=ba:

Critical pair: abba=bb.

Reduce LHS:

Referenced by [6].

Overlap of [5] aabb=bb with [2] abbbbb=b:

Critical pair: ab=bbbbb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.

Referenced by [7], [8].

Overlap of [1] aba=b with [6] ba=ab:

Critical pair: aab=b.

Defines rule #2.

Simplify [4] bbbbb=ba.

Reduce RHS:

Defines rule #3.