Certificate for #24711 ⟨a, b | aa=a, babbbb=ab⟩

Completion settings:

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

Axiom: aa=a.

Defines rule #3.

Referenced by [3], [9], [11].

Axiom: babbbb=ab.

Referenced by [3], [4], [6], [8], [9], [10], [11].

Overlap of [2] babbbb=ab with [2] babbbb=ab:

Critical pair: babbbab=ababbbb.

Reduce RHS:

Referenced by [4], [5].

Overlap of [3] babbbab=ab with [2] babbbb=ab:

Critical pair: babbab=abbbb.

Referenced by [5].

Overlap of [3] babbbab=ab with [3] babbbab=ab:

Critical pair: babbab=abbbab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6], [7].

Overlap of [5] abbbab=abbbb with [2] babbbb=ab:

Critical pair: abbab=abbbbbbb.

Referenced by [7], [8], [9].

Overlap of [5] abbbab=abbbb with [6] abbab=abbbbbbb:

Critical pair: abbbabbbbbbb=abbbbbab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [10].

Overlap of [6] abbab=abbbbbbb with [2] babbbb=ab:

Critical pair: abab=abbbbbbbbbb.

Referenced by [11].

Overlap of [6] abbab=abbbbbbb with [6] abbab=abbbbbbb:

Critical pair: abbabbbbbbb=abbbbbbbbab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [10], [11].

Overlap of [2] babbbb=ab with [9] abbbbbbbbab=ab:

Critical pair: bab=abbbbbab.

Reduce RHS:

Defines rule #2.

Overlap of [9] abbbbbbbbab=ab with [2] babbbb=ab:

Critical pair: abbbbbbbbaab=ababbbb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #1.