Certificate for #2726 ⟨a, b, c | abc=a, bccb=1⟩

Completion settings:

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

Axiom: abc=a.

Defines rule #5.

Referenced by [7].

Axiom: bccb=1.

Referenced by [4].

Axiom: cc=d.

Defines rule #7.

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

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

Critical pair: bdb=1.

Referenced by [5], [8].

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

Critical pair: bd=db.

Flip LHS and RHS.

Defines rule #1.

Referenced by [8], [10], [11].

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

Critical pair: cd=dc.

Flip LHS and RHS.

Defines rule #4.

Referenced by [9].

Overlap of [1] abc=a with [3] cc=d:

Critical pair: abd=ac.

Flip LHS and RHS.

Defines rule #3.

Overlap of [4] bdb=1 with [5] db=bd:

Critical pair: bbd=1.

Defines rule #2.

Referenced by [9], [11].

Overlap of [8] bbd=1 with [6] dc=cd:

Critical pair: bbcd=c.

Referenced by [10].

Overlap of [9] bbcd=c with [5] db=bd:

Critical pair: bbcbd=cb.

Referenced by [11].

Overlap of [10] bbcbd=cb with [5] db=bd:

Critical pair: bbcbbd=cbb.

Reduce LHS:

Defines rule #6.