Certificate for #5920 ⟨a, b, c | ab=a, cab=bc⟩

Back:⟨a, b, c | ab=a, cab=bc⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #2.

Referenced by [2], [4], [5].

[2] bc=ca

Axiom: cab=bc.

Reduce LHS:

[1]c(ab)
⇒ ca

Flip LHS and RHS.

Defines rule #6.

Referenced by [4].

[3] ac=d

Axiom: ac=d.

Defines rule #1.

Referenced by [4], [6].

[4] da=d

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

a b bc

Critical pair: aca=ac.

Reduce LHS:

[3](ac)a
⇒ da

Reduce RHS:

[3](ac)
⇒ d

Defines rule #3.

Referenced by [5], [6].

[5] db=d

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

d a ab

Critical pair: da=db.

Reduce LHS:

[4](da)
⇒ d

Flip LHS and RHS.

Defines rule #5.

[6] dc=dd

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

d a ac

Critical pair: dd=dc.

Flip LHS and RHS.

Defines rule #4.