Certificate for #14827 ⟨a, b | abba=a, babbb=a⟩

Completion settings:

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

Axiom: abba=a.

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

Axiom: babbb=a.

Referenced by [3], [4], [5], [6], [7], [8].

Overlap of [1] abba=a with [2] babbb=a:

Critical pair: aba=abbb.

Referenced by [6].

Overlap of [2] babbb=a with [2] babbb=a:

Critical pair: babba=aabbb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [5].

Overlap of [4] aabbb=ba with [2] babbb=a:

Critical pair: aabba=baabbb.

Reduce LHS:

Reduce RHS:

Referenced by [6], [9].

Overlap of [3] aba=abbb with [2] babbb=a:

Critical pair: aa=abbbbbb.

Reduce LHS:

Referenced by [7], [9].

Overlap of [6] bba=abbbbbb with [2] babbb=a:

Critical pair: ba=abbbbbbbbb.

Defines rule #2.

Referenced by [8].

Overlap of [2] babbb=a with [7] ba=abbbbbbbbb:

Critical pair: abbbbbbbbbbbb=a.

Defines rule #1.

Simplify [5] aa=bba.

Reduce RHS:

Defines rule #3.