Certificate for #17679 ⟨a, b | aaaa=1, babbb=ab⟩

Completion settings:

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

Axiom: aaaa=1.

Defines rule #5.

Referenced by [5], [9], [14].

Axiom: babbb=ab.

Referenced by [3], [4], [7], [10], [11], [12], [15].

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

Critical pair: babbab=ababbb.

Reduce RHS:

Referenced by [4], [5], [6], [8].

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

Critical pair: babab=aabbb.

Referenced by [7], [8].

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

Critical pair: babbaaab=aababbab.

Reduce RHS:

Referenced by [6], [14].

Overlap of [3] babbab=aab with [5] babbaaab=b:

Critical pair: babb=aabbaaab.

Flip LHS and RHS.

Referenced by [9].

Overlap of [4] babab=aabbb with [2] babbb=ab:

Critical pair: baab=aabbbbb.

Defines rule #3.

Referenced by [9], [12].

Overlap of [4] babab=aabbb with [3] babbab=aab:

Critical pair: baaab=aabbbbab.

Referenced by [9], [13].

Simplify [6] aabbaaab=babb.

Reduce LHS:

Referenced by [10].

Overlap of [9] bbbbbbbbab=babb with [2] babbb=ab:

Critical pair: bbbbbbbab=babbbb.

Reduce RHS:

Referenced by [11].

Overlap of [10] bbbbbbbab=abb with [2] babbb=ab:

Critical pair: bbbbbbab=abbbb.

Referenced by [12].

Overlap of [2] babbb=ab with [11] bbbbbbab=abbbb:

Critical pair: baabbbb=abbbbab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [13].

Simplify [8] baaab=aabbbbab.

Reduce RHS:

Defines rule #4.

Referenced by [14].

Overlap of [5] babbaaab=b with [13] baaab=aaabbbbbbbb:

Critical pair: babaaabbbbbbbb=b.

Reduce LHS:

Defines rule #1.

Referenced by [15].

Overlap of [2] babbb=ab with [14] bbbbbbbbbbbbbbbb=b:

Critical pair: bab=abbbbbbbbbbbbbb.

Defines rule #2.