Certificate for #2861 ⟨a, b | aaaabababba=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. bababb=d

Axiom: aaaabababba=1.

Referenced by [4].

Axiom: aaaaa=c.

Defines rule #5.

Referenced by [5], [6], [13], [17], [18], [22], [26], [31], [34].

Axiom: bababb=d.

Defines rule #17.

Referenced by [4], [9], [18], [20].

Overlap of [1] aaaabababba=1 with [3] bababb=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], [22], [23], [28], [30], [35], [36], [37].

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], [24], [26], [31], [34].

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

Critical pair: bababd=dababb.

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], [25], [27], [29], [31], [33].

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

Critical pair: dc=adaaaa.

Reduce RHS:

Defines rule #1.

Referenced by [16], [18], [21], [32].

Simplify [9] bababd=dababb.

Reduce RHS:

Defines rule #9.

Referenced by [15], [16].

Overlap of [14] bababd=adbabb with [12] da=ad:

Critical pair: bababad=adbabba.

Defines rule #11.

Referenced by [27].

Overlap of [14] bababd=adbabb with [13] dc=1:

Critical pair: babab=adbabbc.

Flip LHS and RHS.

Referenced by [17].

Overlap of [2] aaaaa=c with [16] adbabbc=babab:

Critical pair: aaaababab=cdbabbc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [18], [19], [23].

Overlap of [3] bababb=d with [17] babbc=aaaababab:

Critical pair: baaaaababab=dc.

Reduce LHS:

Reduce RHS:

Referenced by [20].

Overlap of [17] babbc=aaaababab with [5] ca=ac:

Critical pair: babbac=aaaabababa.

Defines rule #10.

Referenced by [28].

Overlap of [18] bcbabab=1 with [3] bababb=d:

Critical pair: bcbad=abb.

Referenced by [21].

Overlap of [20] bcbad=abb with [13] dc=1:

Critical pair: bcba=abbc.

Defines rule #6.

Referenced by [22], [23].

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

Critical pair: bcbc=abbcaaaa.

Reduce RHS:

Flip LHS and RHS.

Referenced by [24].

Overlap of [21] bcba=abbc with [17] babbc=aaaababab:

Critical pair: bcaaaababab=abbcbbc.

Reduce LHS:

Flip LHS and RHS.

Referenced by [33].

Overlap of [22] abbaaaac=bcbc with [8] cd=1:

Critical pair: abbaaaa=bcbcd.

Reduce RHS:

Referenced by [25].

Overlap of [12] da=ad with [24] abbaaaa=bcb:

Critical pair: dbcb=adbbaaaa.

Flip LHS and RHS.

Referenced by [26].

Overlap of [2] aaaaa=c with [25] adbbaaaa=dbcb:

Critical pair: aaaadbcb=cdbbaaaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [31].

Overlap of [15] bababad=adbabba with [12] da=ad:

Critical pair: bababaad=adbabbaa.

Defines rule #13.

Referenced by [29].

Overlap of [19] babbac=aaaabababa with [5] ca=ac:

Critical pair: babbaac=aaaabababaa.

Defines rule #12.

Referenced by [30].

Overlap of [27] bababaad=adbabbaa with [12] da=ad:

Critical pair: bababaaad=adbabbaaa.

Defines rule #15.

Referenced by [31].

Overlap of [28] babbaac=aaaabababaa with [5] ca=ac:

Critical pair: babbaaac=aaaabababaaa.

Defines rule #14.

Overlap of [29] bababaaad=adbabbaaa with [12] da=ad:

Critical pair: bababaaaad=adbabbaaaa.

Reduce RHS:

Referenced by [32].

Overlap of [31] bababaaaad=adbbcb with [13] dc=1:

Critical pair: bababaaaa=adbbcbc.

Defines rule #16.

Overlap of [12] da=ad with [23] abbcbbc=baaaacbabab:

Critical pair: dbaaaacbabab=adbbcbbc.

Flip LHS and RHS.

Referenced by [34].

Overlap of [2] aaaaa=c with [33] adbbcbbc=dbaaaacbabab:

Critical pair: aaaadbaaaacbabab=cdbbcbbc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #18.

Referenced by [35].

Overlap of [34] bbcbbc=aaaadbaaaacbabab with [5] ca=ac:

Critical pair: bbcbbac=aaaadbaaaacbababa.

Defines rule #19.

Referenced by [36].

Overlap of [35] bbcbbac=aaaadbaaaacbababa with [5] ca=ac:

Critical pair: bbcbbaac=aaaadbaaaacbababaa.

Defines rule #20.

Referenced by [37].

Overlap of [36] bbcbbaac=aaaadbaaaacbababaa with [5] ca=ac:

Critical pair: bbcbbaaac=aaaadbaaaacbababaaa.

Defines rule #21.