Certificate for #6258 ⟨a, b, c | aa=1, bbccbb=1⟩

Completion settings:

• Auxiliary generators:
  1. d = cc
• Reduction order:
  • Left-to-right shortlex with a < d < b < c

Axiom: aa=1.

Defines rule #1.

Axiom: bbccbb=1.

Referenced by [4].

Axiom: cc=d.

Defines rule #4.

Referenced by [4], [5].

Overlap of [2] bbccbb=1 with [3] cc=d:

Critical pair: bbdbb=1.

Referenced by [6], [7], [8], [9], [12].

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

Critical pair: cd=dc.

Defines rule #3.

Referenced by [10].

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

Critical pair: bbd=dbb.

Referenced by [7], [8], [9], [11].

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

Critical pair: bbdb=bdbb.

Reduce LHS:

Flip LHS and RHS.

Referenced by [9].

Overlap of [4] bbdbb=1 with [6] bbd=dbb:

Critical pair: dbbbb=1.

Defines rule #5.

Referenced by [9], [10].

Overlap of [4] bbdbb=1 with [6] bbd=dbb:

Critical pair: bbdbdbb=bd.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [5] cd=dc with [8] dbbbb=1:

Critical pair: c=dcbbbb.

Flip LHS and RHS.

Referenced by [11].

Overlap of [6] bbd=dbb with [10] dcbbbb=c:

Critical pair: bbc=dbbcbbbb.

Flip LHS and RHS.

Referenced by [12].

Overlap of [4] bbdbb=1 with [11] dbbcbbbb=bbc:

Critical pair: bbbbc=cbbbb.

Flip LHS and RHS.

Defines rule #6.