Certificate for #6513 ⟨a, b | aba=b, abbbb=b⟩

Completion settings:

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

Axiom: aba=b.

Referenced by [3], [4].

Axiom: abbbb=b.

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

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

Critical pair: abb=bba.

Flip LHS and RHS.

Referenced by [5].

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

Critical pair: abb=bbbbb.

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

Simplify [3] bba=abb.

Reduce RHS:

Referenced by [6].

Overlap of [2] abbbb=b with [5] bba=bbbbb:

Critical pair: abbbbbbb=ba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9].

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

Critical pair: bbbbbbb=b.

Defines rule #1.

Referenced by [8], [9].

Overlap of [2] abbbb=b with [7] bbbbbbb=b:

Critical pair: ab=bbbb.

Defines rule #2.

Simplify [6] ba=bbbbbbbbbb.

Reduce RHS:

Defines rule #3.