Certificate for #18715 ⟨a, b | aaa=a, aabbba=b⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #4.

Referenced by [3], [4].

Axiom: aabbba=b.

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

Overlap of [1] aaa=a with [2] aabbba=b:

Critical pair: aab=aabbba.

Reduce RHS:

Defines rule #3.

Referenced by [4], [5].

Overlap of [2] aabbba=b with [1] aaa=a:

Critical pair: aabbba=baa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6].

Overlap of [2] aabbba=b with [3] aab=b:

Critical pair: bbba=b.

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

Simplify [4] baa=bbba.

Reduce RHS:

Referenced by [7].

Overlap of [5] bbba=b with [6] baa=b:

Critical pair: bbb=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [8].

Overlap of [5] bbba=b with [7] ba=bbb:

Critical pair: bbbbb=b.

Defines rule #1.