Certificate for #7249 ⟨a, b | aaa=1, ababbbb=1⟩

Completion settings:

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

Axiom: aaa=1.

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

Axiom: ababbbb=1.

Referenced by [3], [6], [7], [8], [9], [18], [20].

Overlap of [1] aaa=1 with [2] ababbbb=1:

Critical pair: aa=babbbb.

Defines rule #3.

Referenced by [4], [10], [11], [14], [15], [16].

Overlap of [1] aaa=1 with [3] aa=babbbb:

Critical pair: babbbba=1.

Referenced by [5], [10], [12].

Overlap of [4] babbbba=1 with [4] babbbba=1:

Critical pair: babbb=bbbba.

Flip LHS and RHS.

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

Overlap of [2] ababbbb=1 with [5] bbbba=babbb:

Critical pair: abababbb=a.

Referenced by [10].

Overlap of [2] ababbbb=1 with [5] bbbba=babbb:

Critical pair: ababbabbb=ba.

Referenced by [12], [13].

Overlap of [2] ababbbb=1 with [5] bbbba=babbb:

Critical pair: ababbbabbb=bba.

Referenced by [15].

Overlap of [2] ababbbb=1 with [5] bbbba=babbb:

Critical pair: ababbbbabbb=bbba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [11], [15], [16], [19].

Overlap of [1] aaa=1 with [6] abababbb=a:

Critical pair: aaa=bababbb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [11].

Overlap of [10] bababbb=1 with [9] bbba=abbb:

Critical pair: babaabbb=a.

Reduce LHS:

Referenced by [17].

Overlap of [7] ababbabbb=ba with [4] babbbba=1:

Critical pair: abab=baba.

Flip LHS and RHS.

Referenced by [14].

Overlap of [7] ababbabbb=ba with [5] bbbba=babbb:

Critical pair: ababbabbabbb=babba.

Referenced by [16].

Overlap of [12] baba=abab with [12] baba=abab:

Critical pair: baabab=ababba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [16].

Overlap of [8] ababbbabbb=bba with [9] bbba=abbb:

Critical pair: abaabbbbbb=bba.

Reduce LHS:

Referenced by [19].

Overlap of [13] ababbabbabbb=babba with [14] ababba=bbabbabbbb:

Critical pair: bbabbabbbbbbabbb=babba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [17].

Simplify [11] babbabbbbbbb=a.

Reduce LHS:

Referenced by [18], [19].

Overlap of [2] ababbbb=1 with [17] abbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=a:

Critical pair: aba=bbbbbbbbbbbbbbbbbbbbbbbbbb.

Defines rule #4.

Referenced by [20].

Overlap of [17] abbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=a with [9] bbba=abbb:

Critical pair: abbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbb=abba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Overlap of [2] ababbbb=1 with [18] aba=bbbbbbbbbbbbbbbbbbbbbbbbbb:

Critical pair: bbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=1.

Defines rule #1.