Certificate for #8890 ⟨a, b | aa=a, abbbb=ba⟩

Completion settings:

[1] aa=a

Axiom: aa=a.

Defines rule #3.

Referenced by [3].

[2] ba=abbbb

Axiom: abbbb=ba.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3].

[3] abbbbbbbbbbbbbbbb=abbbb

Overlap of [2] ba=abbbb with [1] aa=a:

b a aa

Critical pair: ba=abbbba.

Reduce LHS:

[2](ba)
⇒ abbbb

Reduce RHS:

[2]abbb(ba)
[2]⇒ abb(ba)bbbb
[2]⇒ ab(ba)bbbbbbbb
[2]⇒ a(ba)bbbbbbbbbbbb
[1]⇒ (aa)bbbbbbbbbbbbbbbb
⇒ abbbbbbbbbbbbbbbb

Flip LHS and RHS.

Defines rule #1.