Certificate for #1377 ⟨a, b | aaabbabbba=1⟩

Completion settings:

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

Axiom: aaabbabbba=1.

Referenced by [4].

Axiom: aaaa=c.

Defines rule #5.

Referenced by [5], [6], [13], [17], [18], [22], [25], [29].

Axiom: bbabbb=d.

Defines rule #19.

Referenced by [4], [9], [10], [18], [23].

Overlap of [1] aaabbabbba=1 with [3] bbabbb=d:

Critical pair: aaada=1.

Referenced by [6], [7], [8], [11], [12], [13].

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

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [19], [26].

Overlap of [2] aaaa=c with [4] aaada=1:

Critical pair: a=cda.

Flip LHS and RHS.

Referenced by [8].

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

Critical pair: aaad=aada.

Flip LHS and RHS.

Referenced by [11], [12], [13].

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

Critical pair: cd=aaada.

Reduce RHS:

Defines rule #2.

Referenced by [17], [24], [27], [28], [29].

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

Critical pair: bbabd=dabbb.

Referenced by [14].

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

Critical pair: bbabbd=dbabbb.

Defines rule #15.

Referenced by [21], [22].

Overlap of [4] aaada=1 with [7] aada=aaad:

Critical pair: aaadaaad=ada.

Reduce LHS:

Flip LHS and RHS.

Referenced by [13].

Overlap of [7] aada=aaad with [7] aada=aaad:

Critical pair: aadaaad=aaadada.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [13], [14], [15], [20], [21], [28], [30].

Overlap of [12] da=ad with [2] aaaa=c:

Critical pair: dc=adaaa.

Reduce RHS:

Defines rule #1.

Referenced by [16], [18], [22], [23].

Simplify [9] bbabd=dabbb.

Reduce RHS:

Defines rule #7.

Referenced by [15], [16].

Overlap of [14] bbabd=adbbb with [12] da=ad:

Critical pair: bbabad=adbbba.

Defines rule #10.

Referenced by [20].

Overlap of [14] bbabd=adbbb with [13] dc=1:

Critical pair: bbab=adbbbc.

Flip LHS and RHS.

Referenced by [17].

Overlap of [2] aaaa=c with [16] adbbbc=bbab:

Critical pair: aaabbab=cdbbbc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [18], [19], [22].

Overlap of [3] bbabbb=d with [17] bbbc=aaabbab:

Critical pair: bbaaaabbab=dc.

Reduce LHS:

Reduce RHS:

Referenced by [23].

Overlap of [17] bbbc=aaabbab with [5] ca=ac:

Critical pair: bbbac=aaabbaba.

Defines rule #9.

Referenced by [26].

Overlap of [15] bbabad=adbbba with [12] da=ad:

Critical pair: bbabaad=adbbbaa.

Defines rule #12.

Referenced by [28].

Overlap of [10] bbabbd=dbabbb with [12] da=ad:

Critical pair: bbabbad=dbabbba.

Defines rule #16.

Referenced by [30].

Overlap of [10] bbabbd=dbabbb with [13] dc=1:

Critical pair: bbabb=dbabbbc.

Reduce RHS:

Flip LHS and RHS.

Referenced by [23], [27].

Overlap of [22] dbcbbab=bbabb with [18] bbcbbab=1:

Critical pair: dbcbba=bbabbbcbbab.

Reduce RHS:

Referenced by [24], [25].

Overlap of [8] cd=1 with [23] dbcbba=bbab:

Critical pair: cbbab=bcbba.

Flip LHS and RHS.

Defines rule #8.

Overlap of [23] dbcbba=bbab with [2] aaaa=c:

Critical pair: dbcbbc=bbabaaa.

Flip LHS and RHS.

Defines rule #14.

Referenced by [27], [28].

Overlap of [19] bbbac=aaabbaba with [5] ca=ac:

Critical pair: bbbaac=aaabbabaa.

Defines rule #11.

Overlap of [22] dbcbbab=bbabb with [25] bbabaaa=dbcbbc:

Critical pair: dbcdbcbbc=bbabbaaa.

Reduce LHS:

Flip LHS and RHS.

Defines rule #18.

Overlap of [20] bbabaad=adbbbaa with [12] da=ad:

Critical pair: bbabaaad=adbbbaaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [29].

Overlap of [2] aaaa=c with [28] adbbbaaa=dbcbb:

Critical pair: aaadbcbb=cdbbbaaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #13.

Overlap of [21] bbabbad=dbabbba with [12] da=ad:

Critical pair: bbabbaad=dbabbbaa.

Defines rule #17.