Certificate for #27686 ⟨a, b | aa=1, abbbba=bab⟩

Completion settings:

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

Axiom: aa=1.

Defines rule #5.

Referenced by [3], [4], [10], [15].

Axiom: abbbba=bab.

Defines rule #7.

Referenced by [3], [4], [5], [6], [8], [10], [11], [14].

Overlap of [1] aa=1 with [2] abbbba=bab:

Critical pair: abab=bbbba.

Defines rule #6.

Referenced by [5], [7], [9].

Overlap of [2] abbbba=bab with [1] aa=1:

Critical pair: abbbb=baba.

Flip LHS and RHS.

Defines rule #8.

Referenced by [6], [7], [9].

Overlap of [3] abab=bbbba with [2] abbbba=bab:

Critical pair: abbab=bbbbabbba.

Flip LHS and RHS.

Defines rule #11.

Overlap of [2] abbbba=bab with [4] baba=abbbb:

Critical pair: abbbabbbb=babba.

Flip LHS and RHS.

Defines rule #9.

Referenced by [8], [9].

Overlap of [4] baba=abbbb with [3] abab=bbbba:

Critical pair: bbbbba=abbbbb.

Defines rule #4.

Referenced by [9], [10], [14], [15].

Overlap of [2] abbbba=bab with [6] babba=abbbabbbb:

Critical pair: abbbabbbabbbb=babbba.

Referenced by [9], [12], [13].

Overlap of [6] babba=abbbabbbb with [8] abbbabbbabbbb=babbba:

Critical pair: babbbabbba=abbbabbbbbbbabbbabbbb.

Reduce RHS:

Referenced by [10].

Overlap of [2] abbbba=bab with [9] babbbabbba=bbabbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb:

Critical pair: abbbbbabbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=babbbbabbba.

Reduce LHS:

Reduce RHS:

Referenced by [11], [12].

Overlap of [2] abbbba=bab with [10] bbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=bbbab:

Critical pair: abbbbab=babbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [14], [15].

Overlap of [8] abbbabbbabbbb=babbba with [10] bbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=bbbab:

Critical pair: abbbabbbab=babbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb.

Referenced by [13], [16].

Overlap of [8] abbbabbbabbbb=babbba with [12] abbbabbbab=babbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb:

Critical pair: babbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=babbba.

Defines rule #10.

Referenced by [16].

Overlap of [11] babbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=babb with [7] bbbbba=abbbbb:

Critical pair: babbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbbbb=babbbba.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Overlap of [11] babbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=babb with [7] bbbbba=abbbbb:

Critical pair: babbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbbbb=babbbbba.

Reduce LHS:

Reduce RHS:

Defines rule #1.

Overlap of [12] abbbabbbab=babbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb with [13] babbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=babbba:

Critical pair: abbbabbba=babbbabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb.

Reduce RHS:

Defines rule #12.