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

Completion settings:

Reduction order:
- Left-to-right recursive path with deg(b) = 0; deg(a) = 1

[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.