Certificate for #1364 ⟨a, b | aaababbbba=1⟩

Completion settings:

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

Axiom: aaababbbba=1.

Referenced by [4].

Axiom: aaaa=c.

Defines rule #5.

Referenced by [5], [6], [12], [16], [17], [21], [30].

Axiom: babbbb=d.

Defines rule #17.

Referenced by [4], [9], [17], [20].

Overlap of [1] aaababbbba=1 with [3] babbbb=d:

Critical pair: aaada=1.

Referenced by [6], [7], [8], [10], [11], [12].

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

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [18], [27].

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 [10], [11], [12].

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

Critical pair: cd=aaada.

Reduce RHS:

Defines rule #2.

Referenced by [16], [20], [29], [30].

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

Critical pair: babbbd=dabbbb.

Referenced by [13].

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

Critical pair: aaadaaad=ada.

Reduce LHS:

Flip LHS and RHS.

Referenced by [12].

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 [12], [13], [14], [26], [29].

Overlap of [11] da=ad with [2] aaaa=c:

Critical pair: dc=adaaa.

Reduce RHS:

Defines rule #1.

Referenced by [15], [17], [22], [24], [28].

Simplify [9] babbbd=dabbbb.

Reduce RHS:

Defines rule #10.

Referenced by [14], [15].

Overlap of [13] babbbd=adbbbb with [11] da=ad:

Critical pair: babbbad=adbbbba.

Defines rule #12.

Referenced by [26].

Overlap of [13] babbbd=adbbbb with [12] dc=1:

Critical pair: babbb=adbbbbc.

Flip LHS and RHS.

Referenced by [16].

Overlap of [2] aaaa=c with [15] adbbbbc=babbb:

Critical pair: aaababbb=cdbbbbc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #9.

Referenced by [17], [18].

Overlap of [3] babbbb=d with [16] bbbbc=aaababbb:

Critical pair: baaaababbb=dc.

Reduce LHS:

Reduce RHS:

Referenced by [19].

Overlap of [16] bbbbc=aaababbb with [5] ca=ac:

Critical pair: bbbbac=aaababbba.

Defines rule #11.

Referenced by [27].

Overlap of [17] bcbabbb=1 with [17] bcbabbb=1:

Critical pair: bcbabb=cbabbb.

Referenced by [20], [25].

Overlap of [19] bcbabb=cbabbb with [19] bcbabb=cbabbb:

Critical pair: bcbabcbabbb=cbabbbcbabb.

Reduce LHS:

Reduce RHS:

Defines rule #6.

Referenced by [21], [23].

Overlap of [20] bcba=cbab with [2] aaaa=c:

Critical pair: bcbc=cbabaaa.

Flip LHS and RHS.

Referenced by [22], [23].

Overlap of [12] dc=1 with [21] cbabaaa=bcbc:

Critical pair: dbcbc=babaaa.

Flip LHS and RHS.

Defines rule #7.

Overlap of [20] bcba=cbab with [21] cbabaaa=bcbc:

Critical pair: bbcbc=cbabbaaa.

Flip LHS and RHS.

Referenced by [24], [25].

Overlap of [12] dc=1 with [23] cbabbaaa=bbcbc:

Critical pair: dbbcbc=babbaaa.

Flip LHS and RHS.

Defines rule #8.

Overlap of [19] bcbabb=cbabbb with [23] cbabbaaa=bbcbc:

Critical pair: bbbcbc=cbabbbaaa.

Flip LHS and RHS.

Referenced by [28].

Overlap of [14] babbbad=adbbbba with [11] da=ad:

Critical pair: babbbaad=adbbbbaa.

Defines rule #14.

Referenced by [29].

Overlap of [18] bbbbac=aaababbba with [5] ca=ac:

Critical pair: bbbbaac=aaababbbaa.

Defines rule #13.

Overlap of [12] dc=1 with [25] cbabbbaaa=bbbcbc:

Critical pair: dbbbcbc=babbbaaa.

Flip LHS and RHS.

Defines rule #16.

Referenced by [29].

Overlap of [26] babbbaad=adbbbbaa with [11] da=ad:

Critical pair: babbbaaad=adbbbbaaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [30].

Overlap of [2] aaaa=c with [29] adbbbbaaa=dbbbcb:

Critical pair: aaadbbbcb=cdbbbbaaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #15.