Certificate for #12499 ⟨a, b | abab=aa, abba=b⟩

Completion settings:

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

Axiom: abab=aa.

Referenced by [3], [5].

Axiom: abba=b.

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

Overlap of [2] abba=b with [1] abab=aa:

Critical pair: abbaa=bbab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [4].

Overlap of [2] abba=b with [3] bbab=ba:

Critical pair: aba=bb.

Referenced by [5], [7].

Overlap of [1] abab=aa with [4] aba=bb:

Critical pair: bbb=aa.

Flip LHS and RHS.

Defines rule #3.

Referenced by [6].

Overlap of [2] abba=b with [5] aa=bbb:

Critical pair: abbbbb=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [7].

Overlap of [2] abba=b with [6] ba=abbbbb:

Critical pair: ababbbbb=b.

Reduce LHS:

Defines rule #1.