Certificate for #19503 ⟨a, b | aab=a, bbbbb=bb⟩

Completion settings:

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

Axiom: aab=a.

Referenced by [3], [4], [5], [6], [7].

Axiom: bbbbb=bb.

Defines rule #3.

Referenced by [3].

Overlap of [1] aab=a with [2] bbbbb=bb:

Critical pair: aabb=abbbb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [4].

Overlap of [1] aab=a with [3] abbbb=ab:

Critical pair: aab=abbb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [5].

Overlap of [1] aab=a with [4] abbb=a:

Critical pair: aa=abb.

Flip LHS and RHS.

Referenced by [6].

Overlap of [1] aab=a with [5] abb=aa:

Critical pair: aaa=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [7].

Overlap of [1] aab=a with [6] ab=aaa:

Critical pair: aaaa=a.

Defines rule #1.