Certificate for #2046 ⟨a, b, c | aaaa=1, bccb=1⟩

Completion settings:

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

Axiom: aaaa=1.

Defines rule #1.

Axiom: bccb=1.

Referenced by [4].

Axiom: cb=d.

Defines rule #3.

Referenced by [4], [5], [8], [12].

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

Critical pair: bcd=1.

Defines rule #8.

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

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

Critical pair: c=dcd.

Flip LHS and RHS.

Defines rule #10.

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

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

Critical pair: bcc=cd.

Defines rule #9.

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

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

Critical pair: dcc=ccd.

Flip LHS and RHS.

Defines rule #12.

Referenced by [14].

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

Critical pair: bcd=cdb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [9], [11].

Overlap of [6] bcc=cd with [8] cdb=1:

Critical pair: bc=cddb.

Flip LHS and RHS.

Referenced by [10], [11].

Overlap of [4] bcd=1 with [9] cddb=bc:

Critical pair: bbc=db.

Defines rule #4.

Overlap of [5] dcd=c with [9] cddb=bc:

Critical pair: dbc=cdb.

Reduce RHS:

Defines rule #6.

Referenced by [12].

Overlap of [11] dbc=1 with [3] cb=d:

Critical pair: dbd=b.

Defines rule #5.

Referenced by [13].

Overlap of [12] dbd=b with [12] dbd=b:

Critical pair: dbb=bbd.

Flip LHS and RHS.

Defines rule #2.

Overlap of [6] bcc=cd with [7] ccd=dcc:

Critical pair: bdcc=cdd.

Flip LHS and RHS.

Defines rule #11.