Certificate for #1461 ⟨a, b | aabbbaabba=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. aaa=c
  2. bbbaabb=d

Axiom: aabbbaabba=1.

Referenced by [4].

Axiom: aaa=c.

Defines rule #5.

Referenced by [5], [6], [10], [24], [26], [28], [29], [30], [31], [37].

Axiom: bbbaabb=d.

Referenced by [4], [11], [14].

Overlap of [1] aabbbaabba=1 with [3] bbbaabb=d:

Critical pair: aada=1.

Referenced by [6], [7], [8], [9], [10], [12].

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

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [24], [29], [36], [37].

Overlap of [2] aaa=c with [4] aada=1:

Critical pair: a=cda.

Flip LHS and RHS.

Referenced by [8].

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

Critical pair: aad=ada.

Flip LHS and RHS.

Referenced by [9], [10].

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

Critical pair: cd=aada.

Reduce RHS:

Defines rule #2.

Referenced by [15], [17], [25], [26], [27], [30], [36], [37].

Overlap of [4] aada=1 with [7] ada=aad:

Critical pair: aadaad=da.

Reduce LHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [10], [18], [21], [32], [33], [35].

Overlap of [9] da=ad with [2] aaa=c:

Critical pair: dc=adaa.

Reduce RHS:

Defines rule #1.

Referenced by [13], [22], [23], [32], [34].

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

Critical pair: bbbaad=dbaabb.

Referenced by [12], [13].

Overlap of [11] bbbaad=dbaabb with [4] aada=1:

Critical pair: bbb=dbaabba.

Flip LHS and RHS.

Referenced by [15], [16].

Overlap of [11] bbbaad=dbaabb with [10] dc=1:

Critical pair: bbbaa=dbaabbc.

Referenced by [14], [19], [24], [33].

Overlap of [3] bbbaabb=d with [13] bbbaa=dbaabbc:

Critical pair: dbaabbcbb=d.

Referenced by [17], [18], [20].

Overlap of [8] cd=1 with [12] dbaabba=bbb:

Critical pair: cbbb=baabba.

Flip LHS and RHS.

Defines rule #8.

Referenced by [16], [19], [29].

Overlap of [12] dbaabba=bbb with [15] baabba=cbbb:

Critical pair: dbaabcbbb=bbbabba.

Flip LHS and RHS.

Defines rule #16.

Overlap of [8] cd=1 with [14] dbaabbcbb=d:

Critical pair: cd=baabbcbb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [18].

Overlap of [14] dbaabbcbb=d with [17] baabbcbb=1:

Critical pair: dbaabbcb=daabbcbb.

Reduce RHS:

Referenced by [19], [20].

Overlap of [13] bbbaa=dbaabbc with [15] baabba=cbbb:

Critical pair: bbcbbb=dbaabbcbba.

Reduce RHS:

Flip LHS and RHS.

Referenced by [21].

Overlap of [14] dbaabbcbb=d with [18] dbaabbcb=aadbbcbb:

Critical pair: aadbbcbbb=d.

Referenced by [21].

Overlap of [19] aadbbcbbba=bbcbbb with [20] aadbbcbbb=d:

Critical pair: da=bbcbbb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #13.

Referenced by [22], [35], [36].

Overlap of [21] bbcbbb=ad with [21] bbcbbb=ad:

Critical pair: bbcbad=adcbbb.

Reduce RHS:

Referenced by [23].

Overlap of [22] bbcbad=abbb with [10] dc=1:

Critical pair: bbcba=abbbc.

Defines rule #9.

Referenced by [24], [28].

Overlap of [23] bbcba=abbbc with [2] aaa=c:

Critical pair: bbcbc=abbbcaa.

Reduce RHS:

Flip LHS and RHS.

Referenced by [25].

Overlap of [24] adbaabbcc=bbcbc with [8] cd=1:

Critical pair: adbaabbc=bbcbcd.

Reduce RHS:

Referenced by [26], [27], [28].

Overlap of [2] aaa=c with [25] adbaabbc=bbcb:

Critical pair: aabbcb=cdbaabbc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [29], [30], [33].

Overlap of [25] adbaabbc=bbcb with [8] cd=1:

Critical pair: adbaabb=bbcbd.

Flip LHS and RHS.

Defines rule #7.

Referenced by [30].

Overlap of [25] adbaabbc=bbcb with [23] bbcba=abbbc:

Critical pair: adbaaabbbc=bbcbba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #12.

Overlap of [15] baabba=cbbb with [26] baabbc=aabbcb:

Critical pair: baabaabbcb=cbbbabbc.

Reduce LHS:

Flip LHS and RHS.

Referenced by [34], [35].

Overlap of [26] baabbc=aabbcb with [27] bbcbd=adbaabb:

Critical pair: baaadbaabb=aabbcbbd.

Reduce LHS:

Flip LHS and RHS.

Referenced by [31].

Overlap of [2] aaa=c with [30] aabbcbbd=bbaabb:

Critical pair: abbaabb=cbbcbbd.

Flip LHS and RHS.

Referenced by [32].

Overlap of [10] dc=1 with [31] cbbcbbd=abbaabb:

Critical pair: dabbaabb=bbcbbd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #11.

Simplify [13] bbbaa=dbaabbc.

Reduce RHS:

Defines rule #10.

Referenced by [37].

Overlap of [10] dc=1 with [29] cbbbabbc=bacbbcbb:

Critical pair: dbacbbcbb=bbbabbc.

Flip LHS and RHS.

Defines rule #14.

Overlap of [21] bbcbbb=ad with [29] cbbbabbc=bacbbcbb:

Critical pair: bbbacbbcbb=adabbc.

Reduce RHS:

Referenced by [36].

Overlap of [35] bbbacbbcbb=aadbbc with [21] bbcbbb=ad:

Critical pair: bbbacbbcad=aadbbccbbb.

Reduce LHS:

Defines rule #17.

Referenced by [37].

Overlap of [36] bbbacbba=aadbbccbbb with [2] aaa=c:

Critical pair: bbbacbbc=aadbbccbbbaa.

Reduce RHS:

Defines rule #15.