Certificate for #2819 ⟨a, b | aaaaabababa=1⟩

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(c) = deg(a) = 0, c < a; deg(d) = 1; deg(b) = 2
• Auxiliary generators:
  1. aaaaaa=c
  2. babab=d

Axiom: aaaaabababa=1.

Referenced by [4].

Axiom: aaaaaa=c.

Defines rule #2.

Referenced by [6], [7], [8], [13], [20], [22], [26], [27], [28].

Axiom: babab=d.

Referenced by [4], [5], [14].

Overlap of [1] aaaaabababa=1 with [3] babab=d:

Critical pair: aaaaada=1.

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

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

Critical pair: bad=dab.

Flip LHS and RHS.

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

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

Critical pair: ac=ca.

Defines rule #1.

Referenced by [16], [28], [29].

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

Critical pair: a=cda.

Flip LHS and RHS.

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

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

Critical pair: aa=cada.

Flip LHS and RHS.

Referenced by [13].

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

Critical pair: aaaaad=aaaada.

Referenced by [11], [15].

Overlap of [4] aaaaada=1 with [5] dab=bad:

Critical pair: aaaaabad=b.

Referenced by [16].

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

Critical pair: cd=aaaaada.

Reduce RHS:

Flip LHS and RHS.

Referenced by [15], [17].

Overlap of [7] cda=a with [5] dab=bad:

Critical pair: cbad=ab.

Flip LHS and RHS.

Referenced by [14], [16], [24].

Overlap of [8] cada=aa with [4] aaaaada=1:

Critical pair: cad=aaaaaada.

Reduce RHS:

Referenced by [23].

Overlap of [3] babab=d with [12] ab=cbad:

Critical pair: bcbadab=d.

Reduce LHS:

Referenced by [25].

Overlap of [4] aaaaada=1 with [9] aaaaad=aaaada:

Critical pair: aaaadaa=1.

Reduce LHS:

Defines rule #4.

Referenced by [17], [20], [22].

Overlap of [10] aaaaabad=b with [12] ab=cbad:

Critical pair: aaaacbadad=b.

Reduce LHS:

Referenced by [26].

Simplify [11] aaaadaa=cd.

Reduce RHS:

Referenced by [18], [19], [21].

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

Critical pair: aaaad=aadaa.

Referenced by [19], [20], [21], [22], [26].

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

Critical pair: aaaada=aaadaa.

Reduce LHS:

Flip LHS and RHS.

Referenced by [26].

Overlap of [2] aaaaaa=c with [18] aaaad=aadaa:

Critical pair: aaaadaa=cd.

Reduce LHS:

Reduce RHS:

Referenced by [21].

Overlap of [17] aaaadaa=1 with [18] aaaad=aadaa:

Critical pair: aaaadaadaa=aad.

Reduce LHS:

Flip LHS and RHS.

Referenced by [22], [25], [26].

Overlap of [2] aaaaaa=c with [21] aad=daa:

Critical pair: aaaadaa=cd.

Reduce LHS:

Reduce RHS:

Defines rule #3.

Referenced by [23], [26], [27], [28], [29], [30], [31], [32], [33], [34].

Overlap of [22] dc=1 with [13] cad=a:

Critical pair: da=ad.

Flip LHS and RHS.

Defines rule #5.

Referenced by [24], [25], [26], [28].

Simplify [12] ab=cbad.

Reduce RHS:

Defines rule #6.

Referenced by [28].

Overlap of [14] bcbcbadad=d with [23] ad=da:

Critical pair: bcbcbdaad=d.

Reduce LHS:

Referenced by [27], [28].

Overlap of [16] cccccbadadadadadad=b with [23] ad=da:

Critical pair: cccccbdaadadadadad=b.

Reduce LHS:

Referenced by [30].

Overlap of [25] bcbcbddaa=d with [2] aaaaaa=c:

Critical pair: bcbcbddc=daaaa.

Reduce LHS:

Referenced by [28], [29].

Overlap of [25] bcbcbddaa=d with [24] ab=cbda:

Critical pair: bcbcbddacbda=db.

Reduce LHS:

Flip LHS and RHS.

Defines rule #8.

Overlap of [27] bcbcbd=daaaa with [22] dc=1:

Critical pair: bcbcb=daaaac.

Reduce RHS:

Defines rule #9.

Overlap of [26] cccccbddddd=b with [22] dc=1:

Critical pair: cccccbdddd=bc.

Referenced by [31].

Overlap of [30] cccccbdddd=bc with [22] dc=1:

Critical pair: cccccbddd=bcc.

Referenced by [32].

Overlap of [31] cccccbddd=bcc with [22] dc=1:

Critical pair: cccccbdd=bccc.

Referenced by [33].

Overlap of [32] cccccbdd=bccc with [22] dc=1:

Critical pair: cccccbd=bcccc.

Referenced by [34].

Overlap of [33] cccccbd=bcccc with [22] dc=1:

Critical pair: cccccb=bccccc.

Defines rule #7.