Certificate for #16601 ⟨a, b | aaaa=1, ababbbb=1⟩

Completion settings:

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

Axiom: aaaa=1.

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

Axiom: ababbbb=1.

Referenced by [3], [6], [7], [8], [9], [26], [27], [28], [29].

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

Critical pair: aaa=babbbb.

Defines rule #6.

Referenced by [4], [10], [12], [13], [19], [20], [21].

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

Critical pair: babbbba=1.

Referenced by [5], [10], [14].

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

Critical pair: babbb=bbbba.

Flip LHS and RHS.

Referenced by [6], [7], [8], [9], [13], [15].

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 [13], [14], [15].

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

Critical pair: ababbbabbb=bba.

Referenced by [16].

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], [12], [16], [18], [19], [20], [21], [25], [26].

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

Critical pair: aaaa=bababbb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [11].

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

Critical pair: babaabbb=a.

Referenced by [12].

Overlap of [11] babaabbb=a with [9] bbba=abbb:

Critical pair: babaaabbb=aa.

Reduce LHS:

Referenced by [22].

Overlap of [3] aaa=babbbb with [7] ababbabbb=ba:

Critical pair: aaba=babbbbbabbabbb.

Reduce RHS:

Flip LHS and RHS.

Referenced by [21], [26].

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

Critical pair: abab=baba.

Flip LHS and RHS.

Referenced by [17].

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

Critical pair: ababbabbabbb=babba.

Referenced by [23].

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

Critical pair: abaabbbbbb=bba.

Referenced by [19], [20].

Overlap of [14] baba=abab with [14] baba=abab:

Critical pair: baabab=ababba.

Referenced by [18].

Overlap of [17] baabab=ababba with [9] bbba=abbb:

Critical pair: baabaabbb=ababbabba.

Referenced by [22].

Overlap of [3] aaa=babbbb with [16] abaabbbbbb=bba:

Critical pair: aabba=babbbbbaabbbbbb.

Reduce RHS:

Flip LHS and RHS.

Referenced by [24].

Overlap of [16] abaabbbbbb=bba with [9] bbba=abbb:

Critical pair: abaabbbabbb=bbaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #5.

Referenced by [21], [24], [25].

Overlap of [13] babbabbabbbbbb=aaba with [9] bbba=abbb:

Critical pair: babbabbabbbabbb=aabaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [22].

Simplify [18] baabaabbb=ababbabba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [23].

Overlap of [15] ababbabbabbb=babba with [22] ababbabba=aabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb:

Critical pair: aabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=babba.

Flip LHS and RHS.

Defines rule #4.

Referenced by [26].

Simplify [19] babbaabbbbbbbbb=aabba.

Reduce LHS:

Referenced by [25].

Overlap of [20] bbaa=abbabbbbbbbbbb with [24] baabbabbbbbbbbbbbbbbbbbbb=aabba:

Critical pair: baabba=abbabbbbbbbbbbbbabbbbbbbbbbbbbbbbbbb.

Reduce RHS:

Defines rule #7.

Overlap of [13] babbabbabbbbbb=aaba with [23] babba=aabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb:

Critical pair: aabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbabbbbbb=aaba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [27].

Overlap of [26] aaba=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb with [2] ababbbb=1:

Critical pair: a=abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb.

Flip LHS and RHS.

Referenced by [28].

Overlap of [2] ababbbb=1 with [27] abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=a:

Critical pair: aba=bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb.

Defines rule #3.

Referenced by [29].

Overlap of [2] ababbbb=1 with [28] aba=bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb:

Critical pair: bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=1.

Defines rule #1.