Certificate for #7815 ⟨a, b | aaa=1, babbb=ab⟩

Completion settings:

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

Axiom: aaa=1.

Defines rule #4.

Referenced by [4], [10].

Axiom: babbb=ab.

Referenced by [3], [4], [5], [7], [8], [9].

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

Critical pair: babbab=ababbb.

Reduce RHS:

Referenced by [4], [5], [6].

Overlap of [2] babbb=ab with [3] babbab=aab:

Critical pair: babbaab=ababbab.

Reduce RHS:

Referenced by [6], [8], [10].

Overlap of [3] babbab=aab with [2] babbb=ab:

Critical pair: babab=aabbb.

Referenced by [7], [8].

Overlap of [3] babbab=aab with [4] babbaab=b:

Critical pair: babb=aabbaab.

Flip LHS and RHS.

Referenced by [8].

Overlap of [5] babab=aabbb with [2] babbb=ab:

Critical pair: baab=aabbbbb.

Defines rule #3.

Referenced by [8], [10].

Overlap of [5] babab=aabbb with [4] babbaab=b:

Critical pair: bab=aabbbbaab.

Reduce RHS:

Defines rule #2.

Referenced by [9], [10].

Overlap of [2] babbb=ab with [8] bab=abbbbbbbb:

Critical pair: abbbbbbbbbb=ab.

Referenced by [10].

Overlap of [4] babbaab=b with [8] bab=abbbbbbbb:

Critical pair: abbbbbbbbbaab=b.

Reduce LHS:

Defines rule #1.