Certificate for #5397 ⟨a, b, c | ab=a, bcca=c⟩

Back:⟨a, b, c | ab=a, bcca=c⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3], [4].

[2] bcca=c

Axiom: bcca=c.

Defines rule #4.

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

[3] acca=ac

Overlap of [1] ab=a with [2] bcca=c:

a b bcca

Critical pair: ac=acca.

Flip LHS and RHS.

Defines rule #3.

[4] cb=c

Overlap of [2] bcca=c with [1] ab=a:

bcc a ab

Critical pair: bcca=cb.

Reduce LHS:

[2](bcca)
⇒ c

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] ccca=cc

Overlap of [4] cb=c with [2] bcca=c:

c b bcca

Critical pair: cc=ccca.

Flip LHS and RHS.

Defines rule #5.