Certificate for #1312 ⟨a, b | aaaabaabba=1⟩

Completion settings:

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

Axiom: aaaabaabba=1.

Referenced by [4].

Axiom: aaaaa=c.

Defines rule #5.

Referenced by [5], [6], [13], [17], [18], [21], [26].

Axiom: baabb=d.

Defines rule #15.

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

Overlap of [1] aaaabaabba=1 with [3] baabb=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], [22].

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], [25], [26].

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

Critical pair: baabd=daabb.

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], [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], [23], [25].

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

Critical pair: dc=adaaaa.

Reduce RHS:

Defines rule #1.

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

Simplify [9] baabd=daabb.

Reduce RHS:

Defines rule #7.

Referenced by [15], [16].

Overlap of [14] baabd=aadbb with [12] da=ad:

Critical pair: baabad=aadbba.

Defines rule #9.

Referenced by [23].

Overlap of [14] baabd=aadbb with [13] dc=1:

Critical pair: baab=aadbbc.

Flip LHS and RHS.

Referenced by [17].

Overlap of [2] aaaaa=c with [16] aadbbc=baab:

Critical pair: aaabaab=cdbbc.

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.

Referenced by [18], [19].

Overlap of [3] baabb=d with [17] bbc=aaabaab:

Critical pair: baaaaabaab=dc.

Reduce LHS:

Reduce RHS:

Referenced by [20].

Overlap of [17] bbc=aaabaab with [5] ca=ac:

Critical pair: bbac=aaabaaba.

Defines rule #8.

Referenced by [22].

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

Critical pair: bcbaa=cbaab.

Defines rule #10.

Referenced by [21].

Overlap of [20] bcbaa=cbaab with [2] aaaaa=c:

Critical pair: bcbc=cbaabaaa.

Flip LHS and RHS.

Referenced by [24].

Overlap of [19] bbac=aaabaaba with [5] ca=ac:

Critical pair: bbaac=aaabaabaa.

Defines rule #11.

Overlap of [15] baabad=aadbba with [12] da=ad:

Critical pair: baabaad=aadbbaa.

Defines rule #12.

Referenced by [25].

Overlap of [13] dc=1 with [21] cbaabaaa=bcbc:

Critical pair: dbcbc=baabaaa.

Flip LHS and RHS.

Defines rule #14.

Referenced by [25].

Overlap of [23] baabaad=aadbbaa with [12] da=ad:

Critical pair: baabaaad=aadbbaaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [26].

Overlap of [2] aaaaa=c with [25] aadbbaaa=dbcb:

Critical pair: aaadbcb=cdbbaaa.

Reduce RHS:

Flip LHS and RHS.

Defines rule #13.