Certificate for #2871 ⟨a, b | aaaabbaaaba=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. bbaaab=d

Axiom: aaaabbaaaba=1.

Referenced by [4].

Axiom: aaaaa=c.

Defines rule #5.

Referenced by [5], [6], [13], [20], [21], [24], [31], [33], [41].

Axiom: bbaaab=d.

Referenced by [4], [9], [15], [17].

Overlap of [1] aaaabbaaaba=1 with [3] bbaaab=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 [28], [31], [38], [39], [41], [42].

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 [16], [20], [29], [39], [41].

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

Critical pair: bbaaad=dbaaab.

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], [17], [25], [34], [35], [37].

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

Critical pair: dc=adaaaa.

Reduce RHS:

Defines rule #1.

Referenced by [14], [25], [27], [34], [36], [40].

Overlap of [9] bbaaad=dbaaab with [13] dc=1:

Critical pair: bbaaa=dbaaabc.

Referenced by [15], [17], [18], [22].

Overlap of [3] bbaaab=d with [14] bbaaa=dbaaabc:

Critical pair: dbaaabcb=d.

Referenced by [16].

Overlap of [8] cd=1 with [15] dbaaabcb=d:

Critical pair: cd=baaabcb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [17], [18], [19], [21], [23].

Overlap of [3] bbaaab=d with [16] baaabcb=1:

Critical pair: bbaaa=daaabcb.

Reduce LHS:

Reduce RHS:

Referenced by [18], [22].

Overlap of [14] bbaaa=dbaaabc with [16] baaabcb=1:

Critical pair: b=dbaaabcbcb.

Reduce RHS:

Flip LHS and RHS.

Referenced by [20].

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

Critical pair: baaabc=aaabcb.

Defines rule #6.

Referenced by [21], [23], [28], [29], [30], [31].

Overlap of [2] aaaaa=c with [18] aaadbcbbcb=b:

Critical pair: aab=cdbcbbcb.

Reduce RHS:

Flip LHS and RHS.

Referenced by [21].

Overlap of [20] bcbbcb=aab with [16] baaabcb=1:

Critical pair: bcbbc=aabaaabcb.

Reduce RHS:

Referenced by [26].

Simplify [14] bbaaa=dbaaabc.

Reduce RHS:

Defines rule #12.

Referenced by [41].

Overlap of [16] baaabcb=1 with [19] baaabc=aaabcb:

Critical pair: aaabcbb=1.

Referenced by [24], [30].

Overlap of [2] aaaaa=c with [23] aaabcbb=1:

Critical pair: aa=cbcbb.

Flip LHS and RHS.

Referenced by [25], [26], [30].

Overlap of [13] dc=1 with [24] cbcbb=aa:

Critical pair: daa=bcbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #13.

Referenced by [26], [37], [39].

Overlap of [21] bcbbc=cbcbb with [25] bcbb=aad:

Critical pair: bcbaad=cbcbbbb.

Reduce RHS:

Referenced by [27].

Overlap of [26] bcbaad=aabb with [13] dc=1:

Critical pair: bcbaa=aabbc.

Defines rule #10.

Overlap of [19] baaabc=aaabcb with [5] ca=ac:

Critical pair: baaabac=aaabcba.

Defines rule #8.

Overlap of [19] baaabc=aaabcb with [8] cd=1:

Critical pair: baaab=aaabcbd.

Flip LHS and RHS.

Referenced by [33].

Overlap of [19] baaabc=aaabcb with [24] cbcbb=aa:

Critical pair: baaabaa=aaabcbbcbb.

Reduce RHS:

Defines rule #11.

Referenced by [31], [32].

Overlap of [30] baaabaa=cbb with [19] baaabc=aaabcb:

Critical pair: baaaaaabcb=cbbabc.

Reduce LHS:

Flip LHS and RHS.

Referenced by [36], [37].

Overlap of [30] baaabaa=cbb with [30] baaabaa=cbb:

Critical pair: baaacbb=cbbabaa.

Flip LHS and RHS.

Referenced by [40].

Overlap of [2] aaaaa=c with [29] aaabcbd=baaab:

Critical pair: aabaaab=cbcbd.

Flip LHS and RHS.

Referenced by [34].

Overlap of [13] dc=1 with [33] cbcbd=aabaaab:

Critical pair: daabaaab=bcbd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [35].

Overlap of [34] bcbd=aadbaaab with [12] da=ad:

Critical pair: bcbad=aadbaaaba.

Defines rule #9.

Overlap of [13] dc=1 with [31] cbbabc=bacbcb:

Critical pair: dbacbcb=bbabc.

Flip LHS and RHS.

Defines rule #14.

Referenced by [38].

Overlap of [25] bcbb=aad with [31] cbbabc=bacbcb:

Critical pair: bbacbcb=aadabc.

Reduce RHS:

Referenced by [39].

Overlap of [36] bbabc=dbacbcb with [5] ca=ac:

Critical pair: bbabac=dbacbcba.

Defines rule #16.

Overlap of [37] bbacbcb=aaadbc with [25] bcbb=aad:

Critical pair: bbacbcaad=aaadbccbb.

Reduce LHS:

Defines rule #19.

Referenced by [41].

Overlap of [13] dc=1 with [32] cbbabaa=baaacbb:

Critical pair: dbaaacbb=bbabaa.

Flip LHS and RHS.

Defines rule #18.

Overlap of [39] bbacbaa=aaadbccbb with [2] aaaaa=c:

Critical pair: bbacbc=aaadbccbbaaa.

Reduce RHS:

Defines rule #15.

Referenced by [42].

Overlap of [41] bbacbc=aaadbaaacbcb with [5] ca=ac:

Critical pair: bbacbac=aaadbaaacbcba.

Defines rule #17.