Certificate for #639 ⟨a, b | aaababbba=1⟩

Completion settings:

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

Axiom: aaababbba=1.

Referenced by [4].

Axiom: aaaa=c.

Defines rule #5.

Referenced by [5], [6], [12], [16], [17], [22], [29].

Axiom: babbb=d.

Defines rule #16.

Referenced by [4], [9], [17], [20].

Overlap of [1] aaababbba=1 with [3] babbb=d:

Critical pair: aaada=1.

Referenced by [6], [7], [8], [10], [11], [12].

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

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [18], [26].

Overlap of [2] aaaa=c with [4] aaada=1:

Critical pair: a=cda.

Flip LHS and RHS.

Referenced by [8].

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

Critical pair: aaad=aada.

Flip LHS and RHS.

Referenced by [10], [11], [12].

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

Critical pair: cd=aaada.

Reduce RHS:

Defines rule #2.

Referenced by [16], [28], [29].

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

Critical pair: babbd=dabbb.

Referenced by [13].

Overlap of [4] aaada=1 with [7] aada=aaad:

Critical pair: aaadaaad=ada.

Reduce LHS:

Flip LHS and RHS.

Referenced by [12].

Overlap of [7] aada=aaad with [7] aada=aaad:

Critical pair: aadaaad=aaadada.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [12], [13], [14], [25], [28].

Overlap of [11] da=ad with [2] aaaa=c:

Critical pair: dc=adaaa.

Reduce RHS:

Defines rule #1.

Referenced by [15], [17], [21], [23], [27].

Simplify [9] babbd=dabbb.

Reduce RHS:

Defines rule #9.

Referenced by [14], [15].

Overlap of [13] babbd=adbbb with [11] da=ad:

Critical pair: babbad=adbbba.

Defines rule #11.

Referenced by [25].

Overlap of [13] babbd=adbbb with [12] dc=1:

Critical pair: babb=adbbbc.

Flip LHS and RHS.

Referenced by [16].

Overlap of [2] aaaa=c with [15] adbbbc=babb:

Critical pair: aaababb=cdbbbc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [17], [18].

Overlap of [3] babbb=d with [16] bbbc=aaababb:

Critical pair: baaaababb=dc.

Reduce LHS:

Reduce RHS:

Referenced by [19].

Overlap of [16] bbbc=aaababb with [5] ca=ac:

Critical pair: bbbac=aaababba.

Defines rule #10.

Referenced by [26].

Overlap of [17] bcbabb=1 with [17] bcbabb=1:

Critical pair: bcbab=cbabb.

Referenced by [20], [24].

Overlap of [19] bcbab=cbabb with [3] babbb=d:

Critical pair: bcbad=cbabbabbb.

Reduce RHS:

Referenced by [21].

Overlap of [20] bcbad=cbabd with [12] dc=1:

Critical pair: bcba=cbabdc.

Reduce RHS:

Defines rule #6.

Referenced by [22].

Overlap of [21] bcba=cbab with [2] aaaa=c:

Critical pair: bcbc=cbabaaa.

Flip LHS and RHS.

Referenced by [23], [24].

Overlap of [12] dc=1 with [22] cbabaaa=bcbc:

Critical pair: dbcbc=babaaa.

Flip LHS and RHS.

Defines rule #7.

Overlap of [19] bcbab=cbabb with [22] cbabaaa=bcbc:

Critical pair: bbcbc=cbabbaaa.

Flip LHS and RHS.

Referenced by [27].

Overlap of [14] babbad=adbbba with [11] da=ad:

Critical pair: babbaad=adbbbaa.

Defines rule #13.

Referenced by [28].

Overlap of [18] bbbac=aaababba with [5] ca=ac:

Critical pair: bbbaac=aaababbaa.

Defines rule #12.

Overlap of [12] dc=1 with [24] cbabbaaa=bbcbc:

Critical pair: dbbcbc=babbaaa.

Flip LHS and RHS.

Defines rule #15.

Referenced by [28].

Overlap of [25] babbaad=adbbbaa with [11] da=ad:

Critical pair: babbaaad=adbbbaaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [29].

Overlap of [2] aaaa=c with [28] adbbbaaa=dbbcb:

Critical pair: aaadbbcb=cdbbbaaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #14.