Certificate for #6759 ⟨a, b | aba=a, bbbb=aa⟩

Completion settings:

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

Axiom: aba=a.

Defines rule #3.

Referenced by [4], [5].

Axiom: bbbb=aa.

Defines rule #5.

Referenced by [3], [6].

Overlap of [2] bbbb=aa with [2] bbbb=aa:

Critical pair: baa=aab.

Flip LHS and RHS.

Referenced by [4], [5], [7], [8], [10].

Overlap of [1] aba=a with [3] aab=baa:

Critical pair: abbaa=aab.

Reduce RHS:

Referenced by [7].

Overlap of [3] aab=baa with [1] aba=a:

Critical pair: aa=baaa.

Flip LHS and RHS.

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

Overlap of [2] bbbb=aa with [5] baaa=aa:

Critical pair: bbbaa=aaaaa.

Referenced by [7].

Overlap of [4] abbaa=baa with [3] aab=baa:

Critical pair: abbbaa=baab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [8], [9].

Overlap of [3] aab=baa with [7] bbaa=aaaaaa:

Critical pair: aaaaaaaa=baabaa.

Reduce RHS:

Defines rule #1.

Overlap of [7] bbaa=aaaaaa with [5] baaa=aa:

Critical pair: baa=aaaaaaa.

Defines rule #2.

Referenced by [10].

Simplify [3] aab=baa.

Reduce RHS:

Defines rule #4.