Certificate for #2051 ⟨a, b | aab=a, bbbb=b⟩

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].

Axiom: bbbb=b.

Defines rule #3.

Referenced by [3].

Overlap of [1] aab=a with [2] bbbb=b:

Critical pair: aab=abbb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [4].

Overlap of [1] aab=a with [3] abbb=a:

Critical pair: aa=abb.

Flip LHS and RHS.

Referenced by [5].

Overlap of [1] aab=a with [4] abb=aa:

Critical pair: aaa=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [6].

Overlap of [1] aab=a with [5] ab=aaa:

Critical pair: aaaa=a.

Defines rule #1.