Certificate for #19502 ⟨a, b | aab=a, bbbbb=ba⟩

Completion settings:

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

Axiom: aab=a.

Referenced by [3], [5], [6], [7], [8], [9].

Axiom: bbbbb=ba.

Defines rule #4.

Referenced by [3], [4], [5], [9].

Overlap of [1] aab=a with [2] bbbbb=ba:

Critical pair: aaba=abbbb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6].

Overlap of [2] bbbbb=ba with [2] bbbbb=ba:

Critical pair: bba=bab.

Flip LHS and RHS.

Referenced by [5].

Overlap of [2] bbbbb=ba with [4] bab=bba:

Critical pair: bbbbbba=baab.

Reduce LHS:

Reduce RHS:

Referenced by [10].

Overlap of [1] aab=a with [3] abbbb=aa:

Critical pair: aaa=abbb.

Flip LHS and RHS.

Referenced by [7].

Overlap of [1] aab=a with [6] abbb=aaa:

Critical pair: aaaa=abb.

Flip LHS and RHS.

Referenced by [8], [9].

Overlap of [1] aab=a with [7] abb=aaaa:

Critical pair: aaaaa=ab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [9].

Overlap of [7] abb=aaaa with [2] bbbbb=ba:

Critical pair: aba=aaaabbb.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Referenced by [10].

Overlap of [5] bbaa=ba with [9] aaaaaa=a:

Critical pair: bba=baaaaa.

Defines rule #3.