Certificate for #290 ⟨a, b | aaababba=1⟩

Completion settings:

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

Axiom: aaababba=1.

Referenced by [4].

Axiom: aaaa=c.

Defines rule #5.

Referenced by [5], [6], [12], [16], [17], [20], [25].

Axiom: babb=d.

Defines rule #15.

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

Overlap of [1] aaababba=1 with [3] babb=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], [22].

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], [24], [25].

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

Critical pair: babd=dabb.

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], [21], [24].

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

Critical pair: dc=adaaa.

Reduce RHS:

Defines rule #1.

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

Simplify [9] babd=dabb.

Reduce RHS:

Defines rule #7.

Referenced by [14], [15].

Overlap of [13] babd=adbb with [11] da=ad:

Critical pair: babad=adbba.

Defines rule #10.

Referenced by [21].

Overlap of [13] babd=adbb with [12] dc=1:

Critical pair: bab=adbbc.

Flip LHS and RHS.

Referenced by [16].

Overlap of [2] aaaa=c with [15] adbbc=bab:

Critical pair: aaabab=cdbbc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [17], [18].

Overlap of [3] babb=d with [16] bbc=aaabab:

Critical pair: baaaabab=dc.

Reduce LHS:

Reduce RHS:

Referenced by [19].

Overlap of [16] bbc=aaabab with [5] ca=ac:

Critical pair: bbac=aaababa.

Defines rule #9.

Referenced by [22].

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

Critical pair: bcba=cbab.

Defines rule #8.

Referenced by [20].

Overlap of [19] bcba=cbab with [2] aaaa=c:

Critical pair: bcbc=cbabaaa.

Flip LHS and RHS.

Referenced by [23].

Overlap of [14] babad=adbba with [11] da=ad:

Critical pair: babaad=adbbaa.

Defines rule #12.

Referenced by [24].

Overlap of [18] bbac=aaababa with [5] ca=ac:

Critical pair: bbaac=aaababaa.

Defines rule #11.

Overlap of [12] dc=1 with [20] cbabaaa=bcbc:

Critical pair: dbcbc=babaaa.

Flip LHS and RHS.

Defines rule #14.

Referenced by [24].

Overlap of [21] babaad=adbbaa with [11] da=ad:

Critical pair: babaaad=adbbaaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [25].

Overlap of [2] aaaa=c with [24] adbbaaa=dbcb:

Critical pair: aaadbcb=cdbbaaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #13.