Certificate for #2853 ⟨a, b | aaaabaabbba=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. baabbb=d

Axiom: aaaabaabbba=1.

Referenced by [4].

Axiom: aaaaa=c.

Defines rule #5.

Referenced by [5], [6], [13], [17], [18], [23], [30].

Axiom: baabbb=d.

Defines rule #16.

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

Overlap of [1] aaaabaabbba=1 with [3] baabbb=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], [26].

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], [29], [30].

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

Critical pair: baabbd=daabbb.

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], [14].

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].

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

Critical pair: dc=adaaaa.

Reduce RHS:

Defines rule #1.

Referenced by [16], [18], [22], [24], [28].

Simplify [9] baabbd=daabbb.

Reduce RHS:

Defines rule #9.

Referenced by [15], [16].

Overlap of [14] baabbd=aadbbb with [12] da=ad:

Critical pair: baabbad=aadbbba.

Defines rule #11.

Referenced by [27].

Overlap of [14] baabbd=aadbbb with [13] dc=1:

Critical pair: baabb=aadbbbc.

Flip LHS and RHS.

Referenced by [17].

Overlap of [2] aaaaa=c with [16] aadbbbc=baabb:

Critical pair: aaabaabb=cdbbbc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [18], [19].

Overlap of [3] baabbb=d with [17] bbbc=aaabaabb:

Critical pair: baaaaabaabb=dc.

Reduce LHS:

Reduce RHS:

Referenced by [20].

Overlap of [17] bbbc=aaabaabb with [5] ca=ac:

Critical pair: bbbac=aaabaabba.

Defines rule #10.

Referenced by [26].

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

Critical pair: bcbaab=cbaabb.

Referenced by [21], [25].

Overlap of [20] bcbaab=cbaabb with [3] baabbb=d:

Critical pair: bcbaad=cbaabbaabbb.

Reduce RHS:

Referenced by [22].

Overlap of [21] bcbaad=cbaabd with [13] dc=1:

Critical pair: bcbaa=cbaabdc.

Reduce RHS:

Defines rule #6.

Referenced by [23].

Overlap of [22] bcbaa=cbaab with [2] aaaaa=c:

Critical pair: bcbc=cbaabaaa.

Flip LHS and RHS.

Referenced by [24], [25].

Overlap of [13] dc=1 with [23] cbaabaaa=bcbc:

Critical pair: dbcbc=baabaaa.

Flip LHS and RHS.

Defines rule #7.

Overlap of [20] bcbaab=cbaabb with [23] cbaabaaa=bcbc:

Critical pair: bbcbc=cbaabbaaa.

Flip LHS and RHS.

Referenced by [28].

Overlap of [19] bbbac=aaabaabba with [5] ca=ac:

Critical pair: bbbaac=aaabaabbaa.

Defines rule #12.

Overlap of [15] baabbad=aadbbba with [12] da=ad:

Critical pair: baabbaad=aadbbbaa.

Defines rule #13.

Referenced by [29].

Overlap of [13] dc=1 with [25] cbaabbaaa=bbcbc:

Critical pair: dbbcbc=baabbaaa.

Flip LHS and RHS.

Defines rule #15.

Referenced by [29].

Overlap of [27] baabbaad=aadbbbaa with [12] da=ad:

Critical pair: baabbaaad=aadbbbaaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [30].

Overlap of [2] aaaaa=c with [29] aadbbbaaa=dbbcb:

Critical pair: aaadbbcb=cdbbbaaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #14.