Certificate for #664 ⟨a, b | aabaabbba=1⟩

Completion settings:

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

Axiom: aabaabbba=1.

Referenced by [4].

Axiom: aaa=c.

Defines rule #5.

Referenced by [5], [6], [10], [14], [16], [19], [25], [27], [37].

Axiom: baabbb=d.

Defines rule #13.

Referenced by [4], [11], [16], [18], [24], [29].

Overlap of [1] aabaabbba=1 with [3] baabbb=d:

Critical pair: aada=1.

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

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

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [15], [21], [24], [25], [26], [34].

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], [11].

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

Critical pair: cd=aada.

Reduce RHS:

Defines rule #2.

Referenced by [14], [19], [21], [25], [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], [11], [12], [19], [28], [33].

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

Critical pair: dc=adaa.

Reduce RHS:

Defines rule #1.

Referenced by [13], [16], [20], [22], [23], [33].

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

Critical pair: baabbd=daabbb.

Reduce RHS:

Defines rule #9.

Referenced by [12], [13], [25], [30].

Overlap of [11] baabbd=aadbbb with [9] da=ad:

Critical pair: baabbad=aadbbba.

Referenced by [21].

Overlap of [11] baabbd=aadbbb with [10] dc=1:

Critical pair: baabb=aadbbbc.

Flip LHS and RHS.

Referenced by [14], [15].

Overlap of [2] aaa=c with [13] aadbbbc=baabb:

Critical pair: abaabb=cdbbbc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [16].

Overlap of [13] aadbbbc=baabb with [5] ca=ac:

Critical pair: aadbbbac=baabba.

Referenced by [32].

Overlap of [3] baabbb=d with [14] bbbc=abaabb:

Critical pair: baaabaabb=dc.

Reduce LHS:

Reduce RHS:

Referenced by [17].

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

Critical pair: bcbaab=cbaabb.

Referenced by [18], [21].

Overlap of [17] bcbaab=cbaabb with [3] baabbb=d:

Critical pair: bcbaad=cbaabbaabbb.

Reduce RHS:

Referenced by [19], [20].

Overlap of [18] bcbaad=cbaabd with [9] da=ad:

Critical pair: bcbaaad=cbaabda.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [21], [22].

Overlap of [18] bcbaad=cbaabd with [10] dc=1:

Critical pair: bcbaa=cbaabdc.

Reduce RHS:

Defines rule #7.

Overlap of [17] bcbaab=cbaabb with [19] cbaabad=bcb:

Critical pair: bbcb=cbaabbad.

Reduce RHS:

Flip LHS and RHS.

Referenced by [27], [28], [29], [30], [31].

Overlap of [19] cbaabad=bcb with [10] dc=1:

Critical pair: cbaaba=bcbc.

Referenced by [23], [24], [25], [26].

Overlap of [10] dc=1 with [22] cbaaba=bcbc:

Critical pair: dbcbc=baaba.

Flip LHS and RHS.

Defines rule #6.

Referenced by [26], [31], [34].

Overlap of [22] cbaaba=bcbc with [3] baabbb=d:

Critical pair: cbaad=bcbcabbb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #17.

Overlap of [22] cbaaba=bcbc with [11] baabbd=aadbbb:

Critical pair: cbaaaadbbb=bcbcabbd.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #14.

Overlap of [22] cbaaba=bcbc with [23] baaba=dbcbc:

Critical pair: cbaadbcbc=bcbcaba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #12.

Overlap of [2] aaa=c with [21] aabbba=bbcb:

Critical pair: abbcb=cbbba.

Flip LHS and RHS.

Referenced by [33].

Overlap of [9] da=ad with [21] aabbba=bbcb:

Critical pair: dbbcb=adabbba.

Reduce RHS:

Flip LHS and RHS.

Referenced by [32].

Overlap of [21] aabbba=bbcb with [3] baabbb=d:

Critical pair: aabbd=bbcbabbb.

Flip LHS and RHS.

Defines rule #20.

Overlap of [21] aabbba=bbcb with [11] baabbd=aadbbb:

Critical pair: aabbaadbbb=bbcbabbd.

Flip LHS and RHS.

Defines rule #18.

Overlap of [21] aabbba=bbcb with [23] baaba=dbcbc:

Critical pair: aabbdbcbc=bbcbaba.

Flip LHS and RHS.

Defines rule #16.

Overlap of [15] aadbbbac=baabba with [28] aadbbba=dbbcb:

Critical pair: dbbcbc=baabba.

Flip LHS and RHS.

Defines rule #11.

Referenced by [34], [35].

Overlap of [10] dc=1 with [27] cbbba=abbcb:

Critical pair: dabbcb=bbba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #10.

Referenced by [35].

Overlap of [23] baaba=dbcbc with [32] baabba=dbbcbc:

Critical pair: baadbbcbc=dbcbcabba.

Reduce RHS:

Flip LHS and RHS.

Referenced by [36].

Overlap of [33] bbba=adbbcb with [32] baabba=dbbcbc:

Critical pair: bbdbbcbc=adbbcbabba.

Flip LHS and RHS.

Referenced by [37].

Overlap of [8] cd=1 with [34] dbcbacbba=baadbbcbc:

Critical pair: cbaadbbcbc=bcbacbba.

Flip LHS and RHS.

Defines rule #15.

Overlap of [2] aaa=c with [35] adbbcbabba=bbdbbcbc:

Critical pair: aabbdbbcbc=cdbbcbabba.

Reduce RHS:

Flip LHS and RHS.

Defines rule #19.