Certificate for #2869 ⟨a, b | aaaababbbba=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. aaaaa=c
  2. babbbb=d

Axiom: aaaababbbba=1.

Referenced by [4].

Axiom: aaaaa=c.

Defines rule #5.

Referenced by [5], [6], [13], [17], [18], [22], [33].

Axiom: babbbb=d.

Defines rule #19.

Referenced by [4], [9], [18], [21].

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

Critical pair: aaaada=1.

Referenced by [6], [7], [8], [10], [11], [12], [13].

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

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [19], [28], [31].

Overlap of [2] aaaaa=c with [4] aaaada=1:

Critical pair: a=cda.

Flip LHS and RHS.

Referenced by [8].

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

Critical pair: aaaad=aaada.

Flip LHS and RHS.

Referenced by [10], [11], [12], [13].

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

Critical pair: cd=aaaada.

Reduce RHS:

Defines rule #2.

Referenced by [17], [21], [32], [33].

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

Critical pair: babbbd=dabbbb.

Referenced by [14].

Overlap of [4] aaaada=1 with [7] aaada=aaaad:

Critical pair: aaaadaaaad=aada.

Reduce LHS:

Flip LHS and RHS.

Referenced by [12], [13].

Overlap of [7] aaada=aaaad with [7] aaada=aaaad:

Critical pair: aaadaaaad=aaaadaada.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [12], [13].

Overlap of [11] ada=aad with [4] aaaada=1:

Critical pair: ad=aadaaada.

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [13], [14], [15], [27], [29], [32].

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

Critical pair: dc=adaaaa.

Reduce RHS:

Defines rule #1.

Referenced by [16], [18], [23], [25], [30].

Simplify [9] babbbd=dabbbb.

Reduce RHS:

Defines rule #10.

Referenced by [15], [16].

Overlap of [14] babbbd=adbbbb with [12] da=ad:

Critical pair: babbbad=adbbbba.

Defines rule #12.

Referenced by [27].

Overlap of [14] babbbd=adbbbb with [13] dc=1:

Critical pair: babbb=adbbbbc.

Flip LHS and RHS.

Referenced by [17].

Overlap of [2] aaaaa=c with [16] adbbbbc=babbb:

Critical pair: aaaababbb=cdbbbbc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #9.

Referenced by [18], [19].

Overlap of [3] babbbb=d with [17] bbbbc=aaaababbb:

Critical pair: baaaaababbb=dc.

Reduce LHS:

Reduce RHS:

Referenced by [20].

Overlap of [17] bbbbc=aaaababbb with [5] ca=ac:

Critical pair: bbbbac=aaaababbba.

Defines rule #11.

Referenced by [28].

Overlap of [18] bcbabbb=1 with [18] bcbabbb=1:

Critical pair: bcbabb=cbabbb.

Referenced by [21], [26].

Overlap of [20] bcbabb=cbabbb with [20] bcbabb=cbabbb:

Critical pair: bcbabcbabbb=cbabbbcbabb.

Reduce LHS:

Reduce RHS:

Defines rule #6.

Referenced by [22], [24].

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

Critical pair: bcbc=cbabaaaa.

Flip LHS and RHS.

Referenced by [23], [24].

Overlap of [13] dc=1 with [22] cbabaaaa=bcbc:

Critical pair: dbcbc=babaaaa.

Flip LHS and RHS.

Defines rule #7.

Overlap of [21] bcba=cbab with [22] cbabaaaa=bcbc:

Critical pair: bbcbc=cbabbaaaa.

Flip LHS and RHS.

Referenced by [25], [26].

Overlap of [13] dc=1 with [24] cbabbaaaa=bbcbc:

Critical pair: dbbcbc=babbaaaa.

Flip LHS and RHS.

Defines rule #8.

Overlap of [20] bcbabb=cbabbb with [24] cbabbaaaa=bbcbc:

Critical pair: bbbcbc=cbabbbaaaa.

Flip LHS and RHS.

Referenced by [30].

Overlap of [15] babbbad=adbbbba with [12] da=ad:

Critical pair: babbbaad=adbbbbaa.

Defines rule #14.

Referenced by [29].

Overlap of [19] bbbbac=aaaababbba with [5] ca=ac:

Critical pair: bbbbaac=aaaababbbaa.

Defines rule #13.

Referenced by [31].

Overlap of [27] babbbaad=adbbbbaa with [12] da=ad:

Critical pair: babbbaaad=adbbbbaaa.

Defines rule #16.

Referenced by [32].

Overlap of [13] dc=1 with [26] cbabbbaaaa=bbbcbc:

Critical pair: dbbbcbc=babbbaaaa.

Flip LHS and RHS.

Defines rule #18.

Referenced by [32].

Overlap of [28] bbbbaac=aaaababbbaa with [5] ca=ac:

Critical pair: bbbbaaac=aaaababbbaaa.

Defines rule #15.

Overlap of [29] babbbaaad=adbbbbaaa with [12] da=ad:

Critical pair: babbbaaaad=adbbbbaaaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [33].

Overlap of [2] aaaaa=c with [32] adbbbbaaaa=dbbbcb:

Critical pair: aaaadbbbcb=cdbbbbaaaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #17.