Certificate for #617 ⟨a, b | aaaababba=1⟩

Completion settings:

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

Referenced by [4].

Axiom: aaaaa=c.

Defines rule #5.

Referenced by [6], [7], [14], [17], [18], [21], [28].

Axiom: babb=d.

Defines rule #17.

Referenced by [4], [5], [18].

Overlap of [1] aaaababba=1 with [3] babb=d:

Critical pair: aaaada=1.

Referenced by [7], [8], [9], [10], [11], [12], [14].

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

Critical pair: babd=dabb.

Referenced by [13], [15].

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

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [19], [23], [26].

Overlap of [2] aaaaa=c with [4] aaaada=1:

Critical pair: a=cda.

Flip LHS and RHS.

Referenced by [9].

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

Critical pair: aaaad=aaada.

Flip LHS and RHS.

Referenced by [10], [11], [12], [14].

Overlap of [7] cda=a with [4] aaaada=1:

Critical pair: cd=aaaada.

Reduce RHS:

Defines rule #2.

Referenced by [17], [27], [28].

Overlap of [4] aaaada=1 with [8] aaada=aaaad:

Critical pair: aaaadaaaad=aada.

Reduce LHS:

Flip LHS and RHS.

Referenced by [12], [14].

Overlap of [8] aaada=aaaad with [8] aaada=aaaad:

Critical pair: aaadaaaad=aaaadaada.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [12], [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], [22], [24], [27].

Overlap of [5] babd=dabb with [12] da=ad:

Critical pair: babad=dabba.

Reduce RHS:

Defines rule #10.

Referenced by [22].

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

Critical pair: dc=adaaaa.

Reduce RHS:

Defines rule #1.

Referenced by [16], [18], [25].

Simplify [5] babd=dabb.

Reduce RHS:

Defines rule #7.

Referenced by [16].

Overlap of [15] babd=adbb with [14] dc=1:

Critical pair: bab=adbbc.

Flip LHS and RHS.

Referenced by [17].

Overlap of [2] aaaaa=c with [16] adbbc=bab:

Critical pair: aaaabab=cdbbc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [18], [19].

Overlap of [3] babb=d with [17] bbc=aaaabab:

Critical pair: baaaaabab=dc.

Reduce LHS:

Reduce RHS:

Referenced by [20].

Overlap of [17] bbc=aaaabab with [6] ca=ac:

Critical pair: bbac=aaaababa.

Defines rule #9.

Referenced by [23].

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

Critical pair: bcba=cbab.

Defines rule #8.

Referenced by [21].

Overlap of [20] bcba=cbab with [2] aaaaa=c:

Critical pair: bcbc=cbabaaaa.

Flip LHS and RHS.

Referenced by [25].

Overlap of [13] babad=adbba with [12] da=ad:

Critical pair: babaad=adbbaa.

Defines rule #12.

Referenced by [24].

Overlap of [19] bbac=aaaababa with [6] ca=ac:

Critical pair: bbaac=aaaababaa.

Defines rule #11.

Referenced by [26].

Overlap of [22] babaad=adbbaa with [12] da=ad:

Critical pair: babaaad=adbbaaa.

Defines rule #14.

Referenced by [27].

Overlap of [14] dc=1 with [21] cbabaaaa=bcbc:

Critical pair: dbcbc=babaaaa.

Flip LHS and RHS.

Defines rule #16.

Referenced by [27].

Overlap of [23] bbaac=aaaababaa with [6] ca=ac:

Critical pair: bbaaac=aaaababaaa.

Defines rule #13.

Overlap of [24] babaaad=adbbaaa with [12] da=ad:

Critical pair: babaaaad=adbbaaaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [28].

Overlap of [2] aaaaa=c with [27] adbbaaaa=dbcb:

Critical pair: aaaadbcb=cdbbaaaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #15.