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

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(b) = 0; deg(a) = 1

Axiom: aaba=b.

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

Axiom: abbbb=b.

Referenced by [4], [6], [7], [8], [9].

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

Critical pair: aabb=baba.

Flip LHS and RHS.

Referenced by [5].

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

Critical pair: aabb=bbbbb.

Referenced by [5], [8].

Simplify [3] baba=aabb.

Reduce RHS:

Referenced by [6].

Overlap of [1] aaba=b with [5] baba=bbbbb:

Critical pair: aabbbbb=bba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [2] abbbb=b with [6] bba=abb:

Critical pair: abbabb=ba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [10].

Overlap of [4] aabb=bbbbb with [2] abbbb=b:

Critical pair: ab=bbbbbbb.

Defines rule #2.

Referenced by [9], [10].

Overlap of [2] abbbb=b with [8] ab=bbbbbbb:

Critical pair: bbbbbbbbbb=b.

Defines rule #1.

Simplify [7] ba=ab.

Reduce RHS:

Defines rule #3.