Certificate for #2881 ⟨a, b | aaaabbabbaa=1⟩

Completion settings:

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

Axiom: aaaabbabbaa=1.

Referenced by [4].

Axiom: bba=c.

Referenced by [4], [6].

Axiom: aaaaa=d.

Defines rule #5.

Referenced by [5], [7], [8], [19], [25], [31].

Overlap of [1] aaaabbabbaa=1 with [2] bba=c:

Critical pair: aaaacbbaa=1.

Reduce LHS:

Referenced by [6], [7], [8], [9], [10], [13], [14], [15].

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

Critical pair: ad=da.

Flip LHS and RHS.

Defines rule #2.

Referenced by [16], [21], [25], [26], [29].

Overlap of [2] bba=c with [4] aaaacca=1:

Critical pair: bb=caaacca.

Referenced by [11].

Overlap of [3] aaaaa=d with [4] aaaacca=1:

Critical pair: a=dcca.

Flip LHS and RHS.

Referenced by [10].

Overlap of [4] aaaacca=1 with [3] aaaaa=d:

Critical pair: aaaaccd=aaaa.

Referenced by [13].

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

Critical pair: aaaacc=aaacca.

Flip LHS and RHS.

Referenced by [11].

Overlap of [7] dcca=a with [4] aaaacca=1:

Critical pair: dcc=aaaacca.

Reduce RHS:

Referenced by [17], [19], [20].

Simplify [6] bb=caaacca.

Reduce RHS:

Defines rule #8.

Referenced by [12].

Overlap of [11] bb=caaaacc with [11] bb=caaaacc:

Critical pair: bcaaaacc=caaaaccb.

Referenced by [24].

Overlap of [4] aaaacca=1 with [8] aaaaccd=aaaa:

Critical pair: aaaaccaaaa=aaaccd.

Reduce LHS:

Flip LHS and RHS.

Referenced by [14].

Overlap of [4] aaaacca=1 with [13] aaaccd=aaa:

Critical pair: aaaaccaaa=aaccd.

Reduce LHS:

Flip LHS and RHS.

Referenced by [15].

Overlap of [4] aaaacca=1 with [14] aaccd=aa:

Critical pair: aaaaccaa=accd.

Reduce LHS:

Flip LHS and RHS.

Referenced by [16], [18], [23], [24].

Overlap of [15] accd=a with [5] da=ad:

Critical pair: accad=aa.

Referenced by [17].

Overlap of [16] accad=aa with [10] dcc=1:

Critical pair: acca=aacc.

Referenced by [18].

Overlap of [17] acca=aacc with [15] accd=a:

Critical pair: acca=aaccccd.

Reduce LHS:

Flip LHS and RHS.

Referenced by [19].

Overlap of [3] aaaaa=d with [18] aaccccd=aacc:

Critical pair: aaaaacc=dccccd.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #3.

Referenced by [20], [21], [26], [27], [28], [30], [32].

Overlap of [10] dcc=1 with [19] ccd=1:

Critical pair: dc=cd.

Defines rule #1.

Referenced by [22], [23], [26], [27], [28], [29].

Overlap of [19] ccd=1 with [5] da=ad:

Critical pair: ccad=a.

Referenced by [22].

Overlap of [21] ccad=a with [20] dc=cd:

Critical pair: ccacd=ac.

Referenced by [23].

Overlap of [22] ccacd=ac with [20] dc=cd:

Critical pair: ccaccd=acc.

Reduce LHS:

Defines rule #4.

Referenced by [30], [32].

Overlap of [12] bcaaaacc=caaaaccb with [15] accd=a:

Critical pair: bcaaaa=caaaaccbd.

Defines rule #7.

Referenced by [25].

Overlap of [24] bcaaaa=caaaaccbd with [3] aaaaa=d:

Critical pair: bcd=caaaaccbda.

Reduce RHS:

Flip LHS and RHS.

Referenced by [26].

Overlap of [20] dc=cd with [25] caaaaccbad=bcd:

Critical pair: dbcd=cdaaaaccbad.

Reduce RHS:

Flip LHS and RHS.

Referenced by [27].

Overlap of [26] caaaabad=dbcd with [20] dc=cd:

Critical pair: caaaabacd=dbcdc.

Reduce RHS:

Referenced by [28].

Overlap of [27] caaaabacd=db with [20] dc=cd:

Critical pair: caaaabaccd=dbc.

Reduce LHS:

Referenced by [29].

Overlap of [20] dc=cd with [28] caaaaba=dbc:

Critical pair: ddbc=cdaaaaba.

Reduce RHS:

Flip LHS and RHS.

Referenced by [30].

Overlap of [23] cca=acc with [29] caaaadba=ddbc:

Critical pair: cddbc=accaaadba.

Reduce RHS:

Flip LHS and RHS.

Referenced by [31].

Overlap of [3] aaaaa=d with [30] aaaaba=cddbc:

Critical pair: acddbc=dba.

Flip LHS and RHS.

Referenced by [32].

Overlap of [19] ccd=1 with [31] dba=acddbc:

Critical pair: ccacddbc=ba.

Reduce LHS:

Flip LHS and RHS.

Defines rule #6.