Certificate for #6019 ⟨a, b, c | ab=c, aba=bc⟩

Back:⟨a, b, c | ab=c, aba=bc⟩

Completion settings:

[1] ab=c

Axiom: ab=c.

Defines rule #1.

Referenced by [2], [3], [4].

[2] ca=bc

Axiom: aba=bc.

Reduce LHS:

[1](ab)a
⇒ ca

Defines rule #2.

Referenced by [3].

[3] bcb=cc

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

c a ab

Critical pair: cc=bcb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4].

[4] ccb=acc

Overlap of [1] ab=c with [3] bcb=cc:

a b bcb

Critical pair: acc=ccb.

Flip LHS and RHS.

Defines rule #4.