Certificate for #1320 ⟨a, b | aaaababbba=1⟩

Completion settings:

• Auxiliary generators:
  1. c = aaaaa
  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: aaaababbba=1.

Referenced by [4].

Axiom: aaaaa=c.

Defines rule #5.

Referenced by [5], [6], [13], [17], [18], [23], [32].

Axiom: babbb=d.

Defines rule #18.

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

Overlap of [1] aaaababbba=1 with [3] babbb=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], [27], [30].

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], [31], [32].

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

Critical pair: babbd=dabbb.

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], [14], [15], [26], [28], [31].

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

Critical pair: dc=adaaaa.

Reduce RHS:

Defines rule #1.

Referenced by [16], [18], [22], [24], [29].

Simplify [9] babbd=dabbb.

Reduce RHS:

Defines rule #9.

Referenced by [15], [16].

Overlap of [14] babbd=adbbb with [12] da=ad:

Critical pair: babbad=adbbba.

Defines rule #11.

Referenced by [26].

Overlap of [14] babbd=adbbb with [13] dc=1:

Critical pair: babb=adbbbc.

Flip LHS and RHS.

Referenced by [17].

Overlap of [2] aaaaa=c with [16] adbbbc=babb:

Critical pair: aaaababb=cdbbbc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #8.

Referenced by [18], [19].

Overlap of [3] babbb=d with [17] bbbc=aaaababb:

Critical pair: baaaaababb=dc.

Reduce LHS:

Reduce RHS:

Referenced by [20].

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

Critical pair: bbbac=aaaababba.

Defines rule #10.

Referenced by [27].

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

Critical pair: bcbab=cbabb.

Referenced by [21], [25].

Overlap of [20] bcbab=cbabb with [3] babbb=d:

Critical pair: bcbad=cbabbabbb.

Reduce RHS:

Referenced by [22].

Overlap of [21] bcbad=cbabd with [13] dc=1:

Critical pair: bcba=cbabdc.

Reduce RHS:

Defines rule #6.

Referenced by [23].

Overlap of [22] bcba=cbab with [2] aaaaa=c:

Critical pair: bcbc=cbabaaaa.

Flip LHS and RHS.

Referenced by [24], [25].

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

Critical pair: dbcbc=babaaaa.

Flip LHS and RHS.

Defines rule #7.

Overlap of [20] bcbab=cbabb with [23] cbabaaaa=bcbc:

Critical pair: bbcbc=cbabbaaaa.

Flip LHS and RHS.

Referenced by [29].

Overlap of [15] babbad=adbbba with [12] da=ad:

Critical pair: babbaad=adbbbaa.

Defines rule #13.

Referenced by [28].

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

Critical pair: bbbaac=aaaababbaa.

Defines rule #12.

Referenced by [30].

Overlap of [26] babbaad=adbbbaa with [12] da=ad:

Critical pair: babbaaad=adbbbaaa.

Defines rule #15.

Referenced by [31].

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

Critical pair: dbbcbc=babbaaaa.

Flip LHS and RHS.

Defines rule #17.

Referenced by [31].

Overlap of [27] bbbaac=aaaababbaa with [5] ca=ac:

Critical pair: bbbaaac=aaaababbaaa.

Defines rule #14.

Overlap of [28] babbaaad=adbbbaaa with [12] da=ad:

Critical pair: babbaaaad=adbbbaaaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [32].

Overlap of [2] aaaaa=c with [31] adbbbaaaa=dbbcb:

Critical pair: aaaadbbcb=cdbbbaaaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #16.