Certificate for #3177 ⟨a, b, c | ac=ab, bccb=1⟩

Completion settings:

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

Axiom: ac=ab.

Defines rule #5.

Referenced by [4], [8].

Axiom: bccb=1.

Referenced by [5], [6].

Axiom: cbb=d.

Defines rule #4.

Referenced by [4], [6], [7], [10], [13].

Overlap of [1] ac=ab with [3] cbb=d:

Critical pair: ad=abbb.

Defines rule #1.

Overlap of [2] bccb=1 with [2] bccb=1:

Critical pair: bcc=ccb.

Defines rule #11.

Referenced by [6], [7].

Overlap of [2] bccb=1 with [5] bcc=ccb:

Critical pair: ccbb=1.

Reduce LHS:

Defines rule #9.

Referenced by [7], [8], [9].

Overlap of [3] cbb=d with [5] bcc=ccb:

Critical pair: cbccb=dcc.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [1] ac=ab with [6] cd=1:

Critical pair: a=abd.

Flip LHS and RHS.

Defines rule #2.

Overlap of [7] dcc=c with [6] cd=1:

Critical pair: dc=cd.

Reduce RHS:

Defines rule #8.

Referenced by [10], [11].

Overlap of [9] dc=1 with [3] cbb=d:

Critical pair: dd=bb.

Defines rule #7.

Referenced by [11], [12].

Overlap of [10] dd=bb with [9] dc=1:

Critical pair: d=bbc.

Flip LHS and RHS.

Defines rule #6.

Referenced by [13].

Overlap of [10] dd=bb with [10] dd=bb:

Critical pair: dbb=bbd.

Flip LHS and RHS.

Defines rule #3.

Overlap of [3] cbb=d with [11] bbc=d:

Critical pair: cbd=dbc.

Defines rule #10.