Certificate for #2815 ⟨a, b | aaaaabaabba=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. aaaaaa=c
  2. baabb=d

Axiom: aaaaabaabba=1.

Referenced by [4].

Axiom: aaaaaa=c.

Defines rule #5.

Referenced by [6], [7], [15], [18], [19], [22], [29].

Axiom: baabb=d.

Defines rule #17.

Referenced by [4], [5], [19].

Overlap of [1] aaaaabaabba=1 with [3] baabb=d:

Critical pair: aaaaada=1.

Referenced by [7], [8], [9], [10], [11], [12], [13], [15].

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

Critical pair: baabd=daabb.

Referenced by [14], [16].

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

Critical pair: ac=ca.

Flip LHS and RHS.

Defines rule #3.

Referenced by [20], [24], [27].

Overlap of [2] aaaaaa=c with [4] aaaaada=1:

Critical pair: a=cda.

Flip LHS and RHS.

Referenced by [9].

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

Critical pair: aaaaad=aaaada.

Flip LHS and RHS.

Referenced by [10], [11], [12], [13], [15].

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

Critical pair: cd=aaaaada.

Reduce RHS:

Defines rule #2.

Referenced by [18], [28], [29].

Overlap of [4] aaaaada=1 with [8] aaaada=aaaaad:

Critical pair: aaaaadaaaaad=aaada.

Reduce LHS:

Flip LHS and RHS.

Referenced by [12], [13], [15].

Overlap of [8] aaaada=aaaaad with [8] aaaada=aaaaad:

Critical pair: aaaadaaaaad=aaaaadaaada.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [12], [13], [15].

Overlap of [11] aada=aaad with [4] aaaaada=1:

Critical pair: aad=aaadaaaada.

Reduce RHS:

Flip LHS and RHS.

Referenced by [14], [15], [16].

Overlap of [11] aada=aaad with [8] aaaada=aaaaad:

Critical pair: aadaaaaad=aaadaaada.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [14], [15], [16], [23], [26], [28].

Overlap of [5] baabd=daabb with [13] da=ad:

Critical pair: baabad=daabba.

Reduce RHS:

Defines rule #9.

Referenced by [23].

Overlap of [13] da=ad with [2] aaaaaa=c:

Critical pair: dc=adaaaaa.

Reduce RHS:

Defines rule #1.

Referenced by [17], [19], [25].

Simplify [5] baabd=daabb.

Reduce RHS:

Defines rule #7.

Referenced by [17].

Overlap of [16] baabd=aadbb with [15] dc=1:

Critical pair: baab=aadbbc.

Flip LHS and RHS.

Referenced by [18].

Overlap of [2] aaaaaa=c with [17] aadbbc=baab:

Critical pair: aaaabaab=cdbbc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [19], [20].

Overlap of [3] baabb=d with [18] bbc=aaaabaab:

Critical pair: baaaaaabaab=dc.

Reduce LHS:

Reduce RHS:

Referenced by [21].

Overlap of [18] bbc=aaaabaab with [6] ca=ac:

Critical pair: bbac=aaaabaaba.

Defines rule #8.

Referenced by [24].

Overlap of [19] bcbaab=1 with [19] bcbaab=1:

Critical pair: bcbaa=cbaab.

Defines rule #10.

Referenced by [22].

Overlap of [21] bcbaa=cbaab with [2] aaaaaa=c:

Critical pair: bcbc=cbaabaaaa.

Flip LHS and RHS.

Referenced by [25].

Overlap of [14] baabad=aadbba with [13] da=ad:

Critical pair: baabaad=aadbbaa.

Defines rule #12.

Referenced by [26].

Overlap of [20] bbac=aaaabaaba with [6] ca=ac:

Critical pair: bbaac=aaaabaabaa.

Defines rule #11.

Referenced by [27].

Overlap of [15] dc=1 with [22] cbaabaaaa=bcbc:

Critical pair: dbcbc=baabaaaa.

Flip LHS and RHS.

Defines rule #16.

Referenced by [28].

Overlap of [23] baabaad=aadbbaa with [13] da=ad:

Critical pair: baabaaad=aadbbaaa.

Defines rule #14.

Referenced by [28].

Overlap of [24] bbaac=aaaabaabaa with [6] ca=ac:

Critical pair: bbaaac=aaaabaabaaa.

Defines rule #13.

Overlap of [26] baabaaad=aadbbaaa with [13] da=ad:

Critical pair: baabaaaad=aadbbaaaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [29].

Overlap of [2] aaaaaa=c with [28] aadbbaaaa=dbcb:

Critical pair: aaaadbcb=cdbbaaaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #15.