Certificate for #522 ⟨a, b, c | ac=ab, ba=c⟩

Back:⟨a, b, c | ac=ab, ba=c⟩

Completion settings:

[1] ab=ac

Axiom: ac=ab.

Flip LHS and RHS.

Defines rule #1.

Referenced by [3], [4].

[2] ba=c

Axiom: ba=c.

Defines rule #3.

Referenced by [3], [4], [5].

[3] aca=ac

Overlap of [1] ab=ac with [2] ba=c:

a b ba

Critical pair: ac=aca.

Flip LHS and RHS.

Defines rule #4.

[4] cb=cc

Overlap of [2] ba=c with [1] ab=ac:

b a ab

Critical pair: bac=cb.

Reduce LHS:

[2](ba)c
⇒ cc

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] cca=cc

Overlap of [4] cb=cc with [2] ba=c:

c b ba

Critical pair: cc=cca.

Flip LHS and RHS.

Defines rule #5.