Certificate for #3293 ⟨a, b | abbabbbabba=1⟩

Completion settings:

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

Axiom: abbabbbabba=1.

Referenced by [4].

Axiom: abba=c.

Referenced by [4], [7], [9].

Axiom: bbb=d.

Defines rule #7.

Referenced by [4], [6], [11].

Overlap of [1] abbabbbabba=1 with [2] abba=c:

Critical pair: cbbbabba=1.

Reduce LHS:

Referenced by [5], [8], [10], [12].

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

Critical pair: cd=dc.

Flip LHS and RHS.

Defines rule #1.

Referenced by [8], [12], [14], [16].

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

Critical pair: bd=db.

Flip LHS and RHS.

Defines rule #3.

Referenced by [13].

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

Critical pair: abbc=cbba.

Referenced by [8].

Overlap of [7] abbc=cbba with [4] cdc=1:

Critical pair: abb=cbbadc.

Reduce RHS:

Defines rule #8.

Referenced by [9].

Overlap of [2] abba=c with [8] abb=cbbacd:

Critical pair: cbbacda=c.

Referenced by [10].

Overlap of [4] cdc=1 with [9] cbbacda=c:

Critical pair: cdc=bbacda.

Reduce LHS:

Flip LHS and RHS.

Referenced by [11].

Overlap of [3] bbb=d with [10] bbacda=1:

Critical pair: b=dacda.

Flip LHS and RHS.

Referenced by [15], [18].

Overlap of [4] cdc=1 with [5] dc=cd:

Critical pair: ccd=1.

Defines rule #2.

Referenced by [13], [15], [16], [18].

Overlap of [12] ccd=1 with [6] db=bd:

Critical pair: ccbd=b.

Referenced by [14].

Overlap of [13] ccbd=b with [5] dc=cd:

Critical pair: ccbcd=bc.

Referenced by [16].

Overlap of [12] ccd=1 with [11] dacda=b:

Critical pair: ccb=acda.

Flip LHS and RHS.

Referenced by [17].

Overlap of [14] ccbcd=bc with [5] dc=cd:

Critical pair: ccbccd=bcc.

Reduce LHS:

Defines rule #4.

Referenced by [17].

Simplify [15] acda=ccb.

Reduce RHS:

Defines rule #6.

Referenced by [18].

Overlap of [17] acda=bcc with [11] dacda=b:

Critical pair: acb=bcccda.

Reduce RHS:

Defines rule #5.