Certificate for #14632 ⟨a, b | aaba=b, abbbb=b⟩

Completion settings:

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

Axiom: aaba=b.

Referenced by [3], [4], [7], [9], [11].

Axiom: abbbb=b.

Referenced by [4], [5], [6], [7], [8].

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

Critical pair: aabb=baba.

Flip LHS and RHS.

Referenced by [5], [6], [9].

Overlap of [1] aaba=b with [2] abbbb=b:

Critical pair: aabb=bbbbb.

Flip LHS and RHS.

Referenced by [9].

Overlap of [3] baba=aabb with [2] abbbb=b:

Critical pair: babb=aabbbbbb.

Reduce RHS:

Referenced by [6], [7], [9].

Overlap of [3] baba=aabb with [5] babb=abbb:

Critical pair: baabbb=aabbbb.

Reduce RHS:

Referenced by [7], [8], [9], [10].

Overlap of [1] aaba=b with [6] baabbb=ab:

Critical pair: aaab=babbb.

Reduce RHS:

Defines rule #2.

Referenced by [10], [11].

Overlap of [2] abbbb=b with [6] baabbb=ab:

Critical pair: abbbab=baabbb.

Reduce RHS:

Referenced by [10].

Overlap of [3] baba=aabb with [6] baabbb=ab:

Critical pair: baab=aabbabbb.

Reduce RHS:

Referenced by [10].

Overlap of [6] baabbb=ab with [6] baabbb=ab:

Critical pair: baabbab=abaabbb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Overlap of [7] aaab=b with [1] aaba=b:

Critical pair: ab=ba.

Flip LHS and RHS.

Defines rule #1.