Certificate for #548 ⟨a, b, c | bb=aa, cc=a⟩

Back:⟨a, b, c | bb=aa, cc=a⟩

Completion settings:

[1] aa=bb

Axiom: bb=aa.

Flip LHS and RHS.

Referenced by [3].

[2] a=cc

Axiom: cc=a.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3].

[3] cccc=bb

Overlap of [1] aa=bb with [2] a=cc:

aa a

Critical pair: cca=bb.

Reduce LHS:

[2]cc(a)
⇒ cccc

Defines rule #2.

Referenced by [4].

[4] cbb=bbc

Overlap of [3] cccc=bb with [3] cccc=bb:

c ccc cccc

Critical pair: cbb=bbc.

Defines rule #1.