Certificate for #4900 ⟨a, b, c | ab=a, bcccb=1⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #2.

Referenced by [5], [7].

[2] bcccb=1

Axiom: bcccb=1.

Referenced by [4].

[3] ccc=d

Axiom: ccc=d.

Defines rule #7.

Referenced by [4], [9].

[4] bdb=1

Overlap of [2] bcccb=1 with [3] ccc=d:

b cccb ccc

Critical pair: bdb=1.

Referenced by [5], [6], [8], [12].

[5] adb=a

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

a b bdb

Critical pair: a=adb.

Flip LHS and RHS.

Referenced by [7].

[6] bd=db

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

bd b bdb

Critical pair: bd=db.

Defines rule #3.

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

[7] ad=a

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

a b bd

Critical pair: adb=ad.

Reduce LHS:

[5](adb)
⇒ a

Flip LHS and RHS.

Defines rule #1.

[8] dbb=1

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

bdb bd

Critical pair: dbb=1.

Defines rule #5.

Referenced by [10].

[9] cd=dc

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

c cc ccc

Critical pair: cd=dc.

Defines rule #4.

Referenced by [10].

[10] dcbb=c

Overlap of [9] cd=dc with [8] dbb=1:

c d dbb

Critical pair: c=dcbb.

Flip LHS and RHS.

Referenced by [11].

[11] dbcbb=bc

Overlap of [6] bd=db with [10] dcbb=c:

b d dcbb

Critical pair: bc=dbcbb.

Flip LHS and RHS.

Referenced by [12].

[12] cbb=bbc

Overlap of [4] bdb=1 with [11] dbcbb=bc:

b db dbcbb

Critical pair: bbc=cbb.

Flip LHS and RHS.

Defines rule #6.