Certificate for #3133 ⟨a, b | aabbabbbbba=1⟩

Completion settings:

• Reduction order:
  • Right-to-left recursive path with deg(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
• Auxiliary generators:
  1. aaa=c
  2. bbabbbbb=d

Axiom: aabbabbbbba=1.

Referenced by [4].

Axiom: aaa=c.

Defines rule #5.

Referenced by [5], [6], [10], [15], [16], [22].

Axiom: bbabbbbb=d.

Defines rule #18.

Referenced by [4], [11], [12], [16], [19], [20].

Overlap of [1] aabbabbbbba=1 with [3] bbabbbbb=d:

Critical pair: aada=1.

Referenced by [6], [7], [8], [9], [10].

Overlap of [2] aaa=c with [2] aaa=c:

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [17], [28].

Overlap of [2] aaa=c with [4] aada=1:

Critical pair: a=cda.

Flip LHS and RHS.

Referenced by [8].

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

Critical pair: aad=ada.

Flip LHS and RHS.

Referenced by [9], [10].

Overlap of [6] cda=a with [4] aada=1:

Critical pair: cd=aada.

Reduce RHS:

Defines rule #2.

Referenced by [15], [19], [32].

Overlap of [4] aada=1 with [7] ada=aad:

Critical pair: aadaad=da.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [10], [11], [13], [30].

Overlap of [9] da=ad with [2] aaa=c:

Critical pair: dc=adaa.

Reduce RHS:

Defines rule #1.

Referenced by [14], [16], [21], [23], [26], [29], [33].

Overlap of [3] bbabbbbb=d with [3] bbabbbbb=d:

Critical pair: bbabbbd=dabbbbb.

Reduce RHS:

Defines rule #10.

Referenced by [13], [14].

Overlap of [3] bbabbbbb=d with [3] bbabbbbb=d:

Critical pair: bbabbbbd=dbabbbbb.

Defines rule #15.

Referenced by [30].

Overlap of [11] bbabbbd=adbbbbb with [9] da=ad:

Critical pair: bbabbbad=adbbbbba.

Defines rule #12.

Overlap of [11] bbabbbd=adbbbbb with [10] dc=1:

Critical pair: bbabbb=adbbbbbc.

Flip LHS and RHS.

Referenced by [15].

Overlap of [2] aaa=c with [14] adbbbbbc=bbabbb:

Critical pair: aabbabbb=cdbbbbbc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #9.

Referenced by [16], [17].

Overlap of [3] bbabbbbb=d with [15] bbbbbc=aabbabbb:

Critical pair: bbaaabbabbb=dc.

Reduce LHS:

Reduce RHS:

Referenced by [18], [19].

Overlap of [15] bbbbbc=aabbabbb with [5] ca=ac:

Critical pair: bbbbbac=aabbabbba.

Defines rule #11.

Referenced by [28].

Overlap of [16] bbcbbabbb=1 with [16] bbcbbabbb=1:

Critical pair: bbcbbab=cbbabbb.

Referenced by [19], [24], [27].

Overlap of [16] bbcbbabbb=1 with [18] bbcbbab=cbbabbb:

Critical pair: bbcbbabbcbbabbb=bcbbab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [20], [25].

Overlap of [19] bcbbab=cbbabb with [3] bbabbbbb=d:

Critical pair: bcbbad=cbbabbbabbbbb.

Reduce RHS:

Referenced by [21].

Overlap of [20] bcbbad=cbbabd with [10] dc=1:

Critical pair: bcbba=cbbabdc.

Reduce RHS:

Defines rule #6.

Referenced by [22].

Overlap of [21] bcbba=cbbab with [2] aaa=c:

Critical pair: bcbbc=cbbabaa.

Flip LHS and RHS.

Referenced by [23], [24], [25].

Overlap of [10] dc=1 with [22] cbbabaa=bcbbc:

Critical pair: dbcbbc=bbabaa.

Flip LHS and RHS.

Defines rule #7.

Overlap of [18] bbcbbab=cbbabbb with [22] cbbabaa=bcbbc:

Critical pair: bbbcbbc=cbbabbbaa.

Flip LHS and RHS.

Referenced by [29].

Overlap of [19] bcbbab=cbbabb with [22] cbbabaa=bcbbc:

Critical pair: bbcbbc=cbbabbaa.

Flip LHS and RHS.

Referenced by [26], [27].

Overlap of [10] dc=1 with [25] cbbabbaa=bbcbbc:

Critical pair: dbbcbbc=bbabbaa.

Flip LHS and RHS.

Defines rule #8.

Overlap of [18] bbcbbab=cbbabbb with [25] cbbabbaa=bbcbbc:

Critical pair: bbbbcbbc=cbbabbbbaa.

Flip LHS and RHS.

Referenced by [33].

Overlap of [17] bbbbbac=aabbabbba with [5] ca=ac:

Critical pair: bbbbbaac=aabbabbbaa.

Referenced by [31].

Overlap of [10] dc=1 with [24] cbbabbbaa=bbbcbbc:

Critical pair: dbbbcbbc=bbabbbaa.

Flip LHS and RHS.

Defines rule #14.

Referenced by [31].

Overlap of [12] bbabbbbd=dbabbbbb with [9] da=ad:

Critical pair: bbabbbbad=dbabbbbba.

Defines rule #16.

Simplify [28] bbbbbaac=aabbabbbaa.

Reduce RHS:

Referenced by [32].

Overlap of [31] bbbbbaac=aadbbbcbbc with [8] cd=1:

Critical pair: bbbbbaa=aadbbbcbbcd.

Reduce RHS:

Defines rule #13.

Overlap of [10] dc=1 with [27] cbbabbbbaa=bbbbcbbc:

Critical pair: dbbbbcbbc=bbabbbbaa.

Flip LHS and RHS.

Defines rule #17.