Certificate for #16152 ⟨a, b | aab=ab, aaab=bb⟩

Back:⟨a, b | aab=ab, aaab=bb⟩

Completion settings:

[1] aab=ab

Axiom: aab=ab.

Referenced by [2], [3].

[2] ab=bb

Axiom: aaab=bb.

Reduce LHS:

[1]a(aab)
[1]⇒ (aab)
⇒ ab

Defines rule #1.

Referenced by [3], [4].

[3] aab=bb

Simplify [1] aab=ab.

Reduce RHS:

[2](ab)
⇒ bb

Referenced by [4].

[4] bbb=bb

Overlap of [3] aab=bb with [2] ab=bb:

a ab ab

Critical pair: abb=bb.

Reduce LHS:

[2](ab)b
⇒ bbb

Defines rule #2.