Certificate for #19295 ⟨a, b | aaa=a, babbb=ab⟩

Completion settings:

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

Axiom: aaa=a.

Defines rule #4.

Referenced by [4], [9], [10], [14].

Axiom: babbb=ab.

Referenced by [3], [4], [5], [8], [10], [11].

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

Critical pair: babbab=ababbb.

Reduce RHS:

Referenced by [4], [5], [6], [7], [9], [12].

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

Critical pair: babbaab=ababbab.

Reduce RHS:

Referenced by [7].

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

Critical pair: babab=aabbb.

Referenced by [7], [8], [9], [10], [13], [14].

Overlap of [3] babbab=aab with [3] babbab=aab:

Critical pair: babaab=aabbab.

Referenced by [13].

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

Critical pair: babab=aabbaab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [12].

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

Critical pair: baab=aabbbbb.

Defines rule #3.

Referenced by [14].

Overlap of [5] babab=aabbb with [3] babbab=aab:

Critical pair: baaab=aabbbbab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [13].

Overlap of [5] babab=aabbb with [5] babab=aabbb:

Critical pair: baaabbb=aabbbab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [11], [12], [14].

Overlap of [10] aabbbab=ab with [2] babbb=ab:

Critical pair: aabbab=abbb.

Referenced by [13].

Overlap of [10] aabbbab=ab with [3] babbab=aab:

Critical pair: aabbaab=abbab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [13], [14].

Overlap of [5] babab=aabbb with [12] abbab=aabbb:

Critical pair: babaabbb=aabbbbab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [12] abbab=aabbb with [5] babab=aabbb:

Critical pair: abaabbb=aabbbab.

Reduce LHS:

Reduce RHS:

Defines rule #1.