Certificate for #5938 ⟨a, b, c | ab=a, cba=bc⟩

Back:⟨a, b, c | ab=a, cba=bc⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [4], [5].

[2] bc=cba

Axiom: cba=bc.

Flip LHS and RHS.

Defines rule #5.

Referenced by [4].

[3] ac=d

Axiom: ac=d.

Defines rule #4.

Referenced by [4], [6].

[4] dba=d

Overlap of [1] ab=a with [2] bc=cba:

a b bc

Critical pair: acba=ac.

Reduce LHS:

[3](ac)ba
⇒ dba

Reduce RHS:

[3](ac)
⇒ d

Referenced by [5], [6], [7].

[5] db=d

Overlap of [4] dba=d with [1] ab=a:

db a ab

Critical pair: dba=db.

Reduce LHS:

[4](dba)
⇒ d

Flip LHS and RHS.

Defines rule #3.

Referenced by [6], [7].

[6] dc=dd

Overlap of [4] dba=d with [3] ac=d:

db a ac

Critical pair: dbd=dc.

Reduce LHS:

[5](db)d
⇒ dd

Flip LHS and RHS.

Defines rule #6.

[7] da=d

Overlap of [4] dba=d with [5] db=d:

dba db

Critical pair: da=d.

Defines rule #2.