Certificate for #12369 ⟨a, b | aaba=ab, babb=b⟩

Completion settings:

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

Axiom: aaba=ab.

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

Axiom: babb=b.

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

Overlap of [1] aaba=ab with [2] babb=b:

Critical pair: aab=abbb.

Defines rule #3.

Referenced by [4], [5].

Overlap of [1] aaba=ab with [3] aab=abbb:

Critical pair: abbba=ab.

Referenced by [6].

Overlap of [1] aaba=ab with [3] aab=abbb:

Critical pair: aababbb=abab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [2] babb=b with [4] abbba=ab:

Critical pair: bab=bba.

Flip LHS and RHS.

Referenced by [7].

Overlap of [2] babb=b with [6] bba=bab:

Critical pair: babab=ba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [8].

Overlap of [2] babb=b with [7] ba=bbb:

Critical pair: bbbbb=b.

Defines rule #1.