Certificate for #5874 ⟨a, b, c | ab=a, bbc=bb⟩

Back:⟨a, b, c | ab=a, bbc=bb⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3].

[2] bbc=bb

Axiom: bbc=bb.

Defines rule #3.

Referenced by [3].

[3] ac=a

Overlap of [1] ab=a with [2] bbc=bb:

a b bbc

Critical pair: abb=abc.

Reduce LHS:

[1](ab)b
[1]⇒ (ab)
⇒ a

Reduce RHS:

[1](ab)c
⇒ ac

Flip LHS and RHS.

Defines rule #2.