Certificate for #4873 ⟨a, b, c | ab=a, bbccb=1⟩

Completion settings:

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

Axiom: ab=a.

Defines rule #1.

Referenced by [5], [7].

Axiom: bbccb=1.

Referenced by [4].

Axiom: bcc=d.

Referenced by [4], [9].

Overlap of [2] bbccb=1 with [3] bcc=d:

Critical pair: bdb=1.

Referenced by [5], [6], [8], [9].

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

Critical pair: a=adb.

Flip LHS and RHS.

Referenced by [7].

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

Critical pair: bd=db.

Defines rule #3.

Referenced by [7], [8], [9], [13], [14], [15].

Overlap of [1] ab=a with [6] bd=db:

Critical pair: adb=ad.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [4] bdb=1 with [6] bd=db:

Critical pair: dbb=1.

Defines rule #4.

Referenced by [11], [12], [13], [15].

Overlap of [4] bdb=1 with [3] bcc=d:

Critical pair: bdd=cc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #7.

Referenced by [10].

Overlap of [9] cc=ddb with [9] cc=ddb:

Critical pair: cddb=ddbc.

Referenced by [11].

Overlap of [10] cddb=ddbc with [8] dbb=1:

Critical pair: cd=ddbcb.

Defines rule #5.

Referenced by [12].

Overlap of [11] cd=ddbcb with [8] dbb=1:

Critical pair: c=ddbcbbb.

Flip LHS and RHS.

Referenced by [13].

Overlap of [6] bd=db with [12] ddbcbbb=c:

Critical pair: bc=dbdbcbbb.

Reduce RHS:

Flip LHS and RHS.

Referenced by [14].

Overlap of [6] bd=db with [13] dcbbb=bc:

Critical pair: bbc=dbcbbb.

Flip LHS and RHS.

Referenced by [15].

Overlap of [6] bd=db with [14] dbcbbb=bbc:

Critical pair: bbbc=dbbcbbb.

Reduce RHS:

Flip LHS and RHS.

Defines rule #6.