Certificate for #6270 ⟨a, b, c | aa=1, bcbccb=1⟩

Completion settings:

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

Axiom: aa=1.

Defines rule #1.

Axiom: bcbccb=1.

Referenced by [5].

Axiom: cb=d.

Defines rule #13.

Referenced by [5], [6], [7], [14].

Axiom: bdc=e.

Defines rule #10.

Referenced by [5], [6], [7], [11].

Overlap of [2] bcbccb=1 with [3] cb=d:

Critical pair: bdccb=1.

Reduce LHS:

Defines rule #3.

Referenced by [8], [9], [11], [12], [14], [15].

Overlap of [3] cb=d with [4] bdc=e:

Critical pair: ce=ddc.

Flip LHS and RHS.

Defines rule #4.

Referenced by [8].

Overlap of [4] bdc=e with [3] cb=d:

Critical pair: bdd=eb.

Flip LHS and RHS.

Defines rule #14.

Overlap of [5] ed=1 with [6] ddc=ce:

Critical pair: ece=dc.

Defines rule #6.

Referenced by [9], [10], [15].

Overlap of [8] ece=dc with [5] ed=1:

Critical pair: ec=dcd.

Flip LHS and RHS.

Defines rule #5.

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

Overlap of [8] ece=dc with [8] ece=dc:

Critical pair: ecdc=dcce.

Defines rule #8.

Overlap of [4] bdc=e with [9] dcd=ec:

Critical pair: bec=ed.

Reduce RHS:

Defines rule #11.

Referenced by [16], [17].

Overlap of [5] ed=1 with [9] dcd=ec:

Critical pair: eec=cd.

Defines rule #7.

Referenced by [14], [15].

Overlap of [9] dcd=ec with [9] dcd=ec:

Critical pair: dcec=eccd.

Flip LHS and RHS.

Defines rule #9.

Overlap of [12] eec=cd with [3] cb=d:

Critical pair: eed=cdb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [17].

Overlap of [12] eec=cd with [8] ece=dc:

Critical pair: edc=cde.

Reduce LHS:

Flip LHS and RHS.

Referenced by [16].

Overlap of [11] bec=1 with [15] cde=c:

Critical pair: bec=de.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [11] bec=1 with [14] cdb=e:

Critical pair: bee=db.

Flip LHS and RHS.

Defines rule #12.