Certificate for #3109 ⟨a, b, c | ab=aa, bccb=1⟩

Completion settings:

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

Axiom: ab=aa.

Defines rule #9.

Referenced by [8], [9], [14].

Axiom: bccb=1.

Referenced by [4].

Axiom: cb=d.

Defines rule #2.

Referenced by [4], [5], [10], [15].

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

Critical pair: bcd=1.

Defines rule #5.

Referenced by [5], [6], [8], [10], [12].

Overlap of [3] cb=d with [4] bcd=1:

Critical pair: c=dcd.

Flip LHS and RHS.

Defines rule #4.

Referenced by [6], [7], [13].

Overlap of [4] bcd=1 with [5] dcd=c:

Critical pair: bcc=cd.

Defines rule #3.

Referenced by [9], [10], [11].

Overlap of [5] dcd=c with [5] dcd=c:

Critical pair: dcc=ccd.

Defines rule #1.

Overlap of [1] ab=aa with [4] bcd=1:

Critical pair: a=aacd.

Flip LHS and RHS.

Defines rule #11.

Referenced by [14].

Overlap of [1] ab=aa with [6] bcc=cd:

Critical pair: acd=aacc.

Flip LHS and RHS.

Defines rule #6.

Overlap of [6] bcc=cd with [3] cb=d:

Critical pair: bcd=cdb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [11], [13].

Overlap of [6] bcc=cd with [10] cdb=1:

Critical pair: bc=cddb.

Flip LHS and RHS.

Referenced by [12], [13], [14].

Overlap of [4] bcd=1 with [11] cddb=bc:

Critical pair: bbc=db.

Defines rule #10.

Referenced by [17].

Overlap of [5] dcd=c with [11] cddb=bc:

Critical pair: dbc=cdb.

Reduce RHS:

Defines rule #8.

Referenced by [15].

Overlap of [8] aacd=a with [11] cddb=bc:

Critical pair: aabc=adb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #14.

Overlap of [13] dbc=1 with [3] cb=d:

Critical pair: dbd=b.

Defines rule #12.

Referenced by [16].

Overlap of [15] dbd=b with [15] dbd=b:

Critical pair: dbb=bbd.

Defines rule #15.

Referenced by [17].

Overlap of [16] dbb=bbd with [12] bbc=db:

Critical pair: ddb=bbdc.

Defines rule #13.