Certificate for #8632 ⟨a, b | aa=a, babbbb=a⟩

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], [4], [5], [8].

Axiom: babbbb=a.

Referenced by [3], [4], [6], [7], [8], [9], [13], [14].

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

Critical pair: babbba=aabbbb.

Reduce RHS:

Referenced by [4], [5], [6], [13].

Overlap of [2] babbbb=a with [3] babbba=abbbb:

Critical pair: babbbabbbb=aabbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [10].

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

Critical pair: babbba=abbbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6].

Overlap of [5] abbbba=abbbb with [3] babbba=abbbb:

Critical pair: abbbabbbb=abbbbbbba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7], [10], [11].

Overlap of [6] abbbbbbba=abba with [2] babbbb=a:

Critical pair: abbbbbba=abbabbbb.

Reduce RHS:

Referenced by [8], [11], [12].

Overlap of [7] abbbbbba=aba with [2] babbbb=a:

Critical pair: abbbbba=ababbbb.

Reduce RHS:

Referenced by [9].

Overlap of [2] babbbb=a with [8] abbbbba=a:

Critical pair: ba=aba.

Flip LHS and RHS.

Referenced by [10], [11], [12].

Overlap of [6] abbbbbbba=abba with [9] aba=ba:

Critical pair: abbbbbbbba=abbaba.

Reduce RHS:

Referenced by [12], [13].

Overlap of [7] abbbbbba=aba with [9] aba=ba:

Critical pair: abbbbbbba=ababa.

Reduce LHS:

Reduce RHS:

Referenced by [12].

Overlap of [7] abbbbbba=aba with [11] abba=bba:

Critical pair: abbbbbbbba=ababba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [13].

Overlap of [12] bbba=abbbbbbbb with [3] babbba=abbbb:

Critical pair: bbabbbb=abbbbbbbbbbba.

Reduce LHS:

Reduce RHS:

Defines rule #2.

Referenced by [14].

Overlap of [2] babbbb=a with [13] ba=abbbbbbbbbbbbbbbb:

Critical pair: abbbbbbbbbbbbbbbbbbbb=a.

Defines rule #1.