Certificate for #12241 ⟨a, b | aaab=aa, bbbb=b⟩

Completion settings:

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

Axiom: aaab=aa.

Referenced by [3], [4], [5], [6].

Axiom: bbbb=b.

Defines rule #3.

Referenced by [3].

Overlap of [1] aaab=aa with [2] bbbb=b:

Critical pair: aaab=aabbb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [4].

Overlap of [1] aaab=aa with [3] aabbb=aa:

Critical pair: aaa=aabb.

Flip LHS and RHS.

Referenced by [5].

Overlap of [1] aaab=aa with [4] aabb=aaa:

Critical pair: aaaa=aab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [6].

Overlap of [1] aaab=aa with [5] aab=aaaa:

Critical pair: aaaaa=aa.

Defines rule #1.