Certificate for #24184 ⟨a, b | aa=a, bbbabbb=a⟩

Back:⟨a, b | aa=a, bbbabbb=a⟩

Completion settings:

[1] aa=a

Axiom: aa=a.

Defines rule #1.

Referenced by [3].

[2] bbbabbb=a

Axiom: bbbabbb=a.

Referenced by [3], [4].

[3] bbba=abbb

Overlap of [2] bbbabbb=a with [2] bbbabbb=a:

bbba bbb bbbabbb

Critical pair: bbbaa=aabbb.

Reduce LHS:

[1]bbb(aa)
⇒ bbba

Reduce RHS:

[1](aa)bbb
⇒ abbb

Defines rule #2.

Referenced by [4].

[4] abbbbbb=a

Overlap of [2] bbbabbb=a with [3] bbba=abbb:

bbbabbb bbba

Critical pair: abbbbbb=a.

Defines rule #3.