Certificate for #2879 ⟨a, b, c | aab=a, bbc=b⟩

Back:⟨a, b, c | aab=a, bbc=b⟩

Completion settings:

[1] aab=a

Axiom: aab=a.

Defines rule #2.

Referenced by [3], [4].

[2] bbc=b

Axiom: bbc=b.

Defines rule #4.

Referenced by [3].

[3] abc=a

Overlap of [1] aab=a with [2] bbc=b:

aa b bbc

Critical pair: aab=abc.

Reduce LHS:

[1](aab)
⇒ a

Flip LHS and RHS.

Defines rule #3.

Referenced by [4].

[4] ac=aa

Overlap of [1] aab=a with [3] abc=a:

a ab abc

Critical pair: aa=ac.

Flip LHS and RHS.

Defines rule #1.