Certificate for #2953 ⟨a, b | aaababbbbba=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. aaaa=c
  2. babbbbb=d

Axiom: aaababbbbba=1.

Referenced by [4].

Axiom: aaaa=c.

Defines rule #5.

Referenced by [5], [6], [11], [15], [16], [22], [33].

Axiom: babbbbb=d.

Defines rule #18.

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

Overlap of [1] aaababbbbba=1 with [3] babbbbb=d:

Critical pair: aaada=1.

Referenced by [6], [7], [8], [9], [10], [11].

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

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [17], [30].

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 [9], [10], [11].

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

Critical pair: cd=aaada.

Reduce RHS:

Defines rule #2.

Referenced by [15], [19], [32], [33].

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

Critical pair: aaadaaad=ada.

Reduce LHS:

Flip LHS and RHS.

Referenced by [11].

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 [11], [12], [13], [29], [32].

Overlap of [10] da=ad with [2] aaaa=c:

Critical pair: dc=adaaa.

Reduce RHS:

Defines rule #1.

Referenced by [14], [16], [21], [23], [25], [27], [31].

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

Critical pair: babbbbd=dabbbbb.

Reduce RHS:

Defines rule #11.

Referenced by [13], [14].

Overlap of [12] babbbbd=adbbbbb with [10] da=ad:

Critical pair: babbbbad=adbbbbba.

Defines rule #13.

Referenced by [29].

Overlap of [12] babbbbd=adbbbbb with [11] dc=1:

Critical pair: babbbb=adbbbbbc.

Flip LHS and RHS.

Referenced by [15].

Overlap of [2] aaaa=c with [14] adbbbbbc=babbbb:

Critical pair: aaababbbb=cdbbbbbc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #10.

Referenced by [16], [17].

Overlap of [3] babbbbb=d with [15] bbbbbc=aaababbbb:

Critical pair: baaaababbbb=dc.

Reduce LHS:

Reduce RHS:

Referenced by [18].

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

Critical pair: bbbbbac=aaababbbba.

Defines rule #12.

Referenced by [30].

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

Critical pair: bcbabbb=cbabbbb.

Referenced by [19].

Overlap of [18] bcbabbb=cbabbbb with [18] bcbabbb=cbabbbb:

Critical pair: bcbabbcbabbbb=cbabbbbcbabbb.

Reduce LHS:

Reduce RHS:

Referenced by [20], [24], [26].

Overlap of [19] bcbab=cbabb with [3] babbbbb=d:

Critical pair: bcbad=cbabbabbbbb.

Reduce RHS:

Referenced by [21].

Overlap of [20] bcbad=cbabd with [11] dc=1:

Critical pair: bcba=cbabdc.

Reduce RHS:

Defines rule #6.

Referenced by [22], [28].

Overlap of [21] bcba=cbab with [2] aaaa=c:

Critical pair: bcbc=cbabaaa.

Flip LHS and RHS.

Referenced by [23], [24].

Overlap of [11] dc=1 with [22] cbabaaa=bcbc:

Critical pair: dbcbc=babaaa.

Flip LHS and RHS.

Defines rule #7.

Overlap of [19] bcbab=cbabb with [22] cbabaaa=bcbc:

Critical pair: bbcbc=cbabbaaa.

Flip LHS and RHS.

Referenced by [25], [26].

Overlap of [11] dc=1 with [24] cbabbaaa=bbcbc:

Critical pair: dbbcbc=babbaaa.

Flip LHS and RHS.

Defines rule #8.

Overlap of [19] bcbab=cbabb with [24] cbabbaaa=bbcbc:

Critical pair: bbbcbc=cbabbbaaa.

Flip LHS and RHS.

Referenced by [27], [28].

Overlap of [11] dc=1 with [26] cbabbbaaa=bbbcbc:

Critical pair: dbbbcbc=babbbaaa.

Flip LHS and RHS.

Defines rule #9.

Overlap of [21] bcba=cbab with [26] cbabbbaaa=bbbcbc:

Critical pair: bbbbcbc=cbabbbbaaa.

Flip LHS and RHS.

Referenced by [31].

Overlap of [13] babbbbad=adbbbbba with [10] da=ad:

Critical pair: babbbbaad=adbbbbbaa.

Defines rule #15.

Referenced by [32].

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

Critical pair: bbbbbaac=aaababbbbaa.

Defines rule #14.

Overlap of [11] dc=1 with [28] cbabbbbaaa=bbbbcbc:

Critical pair: dbbbbcbc=babbbbaaa.

Flip LHS and RHS.

Defines rule #17.

Referenced by [32].

Overlap of [29] babbbbaad=adbbbbbaa with [10] da=ad:

Critical pair: babbbbaaad=adbbbbbaaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [33].

Overlap of [2] aaaa=c with [32] adbbbbbaaa=dbbbbcb:

Critical pair: aaadbbbbcb=cdbbbbbaaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #16.