Certificate for #17156 ⟨a, b | aaaa=1, bbabbb=a⟩

Completion settings:

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

Axiom: aaaa=1.

Defines rule #3.

Referenced by [5], [6], [9], [11], [14], [16], [17], [18], [19], [21], [23], [24], [37], [39].

Axiom: bbabbb=a.

Referenced by [3], [4], [7], [10], [15], [16], [21], [23], [25], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36].

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

Critical pair: bbaba=aabbb.

Referenced by [5], [12], [13], [15], [16], [20], [21], [23], [24].

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

Critical pair: bbabba=ababbb.

Referenced by [6], [7].

Overlap of [3] bbaba=aabbb with [1] aaaa=1:

Critical pair: bbab=aabbbaaa.

Flip LHS and RHS.

Referenced by [8].

Overlap of [4] bbabba=ababbb with [1] aaaa=1:

Critical pair: bbabb=ababbbaaa.

Flip LHS and RHS.

Referenced by [13].

Overlap of [4] bbabba=ababbb with [2] bbabbb=a:

Critical pair: bbaa=ababbbbbb.

Referenced by [8], [13], [15], [16], [21], [22], [23], [24], [26].

Simplify [5] aabbbaaa=bbab.

Reduce LHS:

Referenced by [9], [10].

Overlap of [1] aaaa=1 with [8] aabababbbbbba=bbab:

Critical pair: aabbab=bababbbbbba.

Flip LHS and RHS.

Referenced by [13], [20], [21].

Overlap of [8] aabababbbbbba=bbab with [2] bbabbb=a:

Critical pair: aabababbbba=bbabbbb.

Reduce RHS:

Referenced by [11].

Overlap of [1] aaaa=1 with [10] aabababbbba=ab:

Critical pair: aaab=bababbbba.

Flip LHS and RHS.

Referenced by [12], [16].

Overlap of [3] bbaba=aabbb with [11] bababbbba=aaab:

Critical pair: baaab=aabbbbbbba.

Referenced by [13], [15], [16], [17], [19], [21], [23].

Simplify [6] ababbbaaa=bbabb.

Reduce LHS:

Referenced by [14].

Overlap of [1] aaaa=1 with [13] aaabaabbbbbbbbbbbbb=bbabb:

Critical pair: abbabb=baabbbbbbbbbbbbb.

Flip LHS and RHS.

Referenced by [23], [24].

Overlap of [3] bbaba=aabbb with [12] baaab=aabbbbbbba:

Critical pair: bbaaabbbbbbba=aabbbaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [16].

Overlap of [12] baaab=aabbbbbbba with [11] bababbbba=aaab:

Critical pair: baaaaaab=aabbbbbbbaababbbba.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [18], [19].

Overlap of [12] baaab=aabbbbbbba with [12] baaab=aabbbbbbba:

Critical pair: baaaaabbbbbbba=aabbbbbbbaaaab.

Reduce LHS:

Reduce RHS:

Referenced by [27].

Overlap of [1] aaaa=1 with [16] aaabaaba=baab:

Critical pair: abaab=baaba.

Flip LHS and RHS.

Referenced by [19], [21], [24].

Overlap of [16] aaabaaba=baab with [12] baaab=aabbbbbbba:

Critical pair: aaabaaaabbbbbbba=baabaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [21], [24].

Overlap of [3] bbaba=aabbb with [9] bababbbbbba=aabbab:

Critical pair: baabbab=aabbbbbbbbba.

Referenced by [22], [23], [24].

Overlap of [12] baaab=aabbbbbbba with [9] bababbbbbba=aabbab:

Critical pair: baaaaabbab=aabbbbbbbaababbbbbba.

Reduce LHS:

Reduce RHS:

Referenced by [24].

Overlap of [7] bbaa=ababbbbbb with [20] baabbab=aabbbbbbbbba:

Critical pair: baabbbbbbbbba=ababbbbbbbbab.

Referenced by [23].

Overlap of [12] baaab=aabbbbbbba with [20] baabbab=aabbbbbbbbba:

Critical pair: baaaaabbbbbbbbba=aabbbbbbbaaabbab.

Reduce LHS:

Reduce RHS:

Referenced by [25].

Overlap of [18] baaba=abaab with [20] baabbab=aabbbbbbbbba:

Critical pair: baaaabbbbbbbbba=abaababbab.

Reduce LHS:

Reduce RHS:

Referenced by [32].

Overlap of [2] bbabbb=a with [23] babbbbbbbbba=aabbbbb:

Critical pair: baabbbbb=abbbbbba.

Referenced by [26].

Overlap of [7] bbaa=ababbbbbb with [25] baabbbbb=abbbbbba:

Critical pair: babbbbbba=ababbbbbbbbbbb.

Referenced by [30].

Overlap of [17] babbbbbbba=aabbbbbbbb with [2] bbabbb=a:

Critical pair: babbbbba=aabbbbbbbbbbb.

Referenced by [28].

Overlap of [27] babbbbba=aabbbbbbbbbbb with [2] bbabbb=a:

Critical pair: babbba=aabbbbbbbbbbbbbb.

Referenced by [29].

Overlap of [28] babbba=aabbbbbbbbbbbbbb with [2] bbabbb=a:

Critical pair: baba=aabbbbbbbbbbbbbbbbb.

Referenced by [31].

Overlap of [26] babbbbbba=ababbbbbbbbbbb with [2] bbabbb=a:

Critical pair: babbbba=ababbbbbbbbbbbbbb.

Referenced by [31].

Overlap of [2] bbabbb=a with [30] babbbba=ababbbbbbbbbbbbbb:

Critical pair: bababbbbbbbbbbbbbb=aba.

Reduce LHS:

Flip LHS and RHS.

Referenced by [37].

Overlap of [24] bbbbbbbbbba=babbbbbbbbbbbbbbbbbbb with [2] bbabbb=a:

Critical pair: bbbbbbbba=babbbbbbbbbbbbbbbbbbbbbb.

Referenced by [33].

Overlap of [32] bbbbbbbba=babbbbbbbbbbbbbbbbbbbbbb with [2] bbabbb=a:

Critical pair: bbbbbba=babbbbbbbbbbbbbbbbbbbbbbbbb.

Referenced by [34].

Overlap of [33] bbbbbba=babbbbbbbbbbbbbbbbbbbbbbbbb with [2] bbabbb=a:

Critical pair: bbbba=babbbbbbbbbbbbbbbbbbbbbbbbbbbb.

Referenced by [35].

Overlap of [34] bbbba=babbbbbbbbbbbbbbbbbbbbbbbbbbbb with [2] bbabbb=a:

Critical pair: bba=babbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb.

Referenced by [36].

Overlap of [2] bbabbb=a with [35] bba=babbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb:

Critical pair: babbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=a.

Referenced by [38].

Overlap of [1] aaaa=1 with [31] aba=aabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb:

Critical pair: aaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=ba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Referenced by [38].

Simplify [36] babbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=a.

Reduce LHS:

Referenced by [39].

Overlap of [1] aaaa=1 with [38] abbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb=a:

Critical pair: aaaa=bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #1.