Certificate for #9161 ⟨a, b | aa=a, abbb=bab⟩

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] bab=abbb

Axiom: abbb=bab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3].

[3] abbbbbbb=abbbbb

Overlap of [2] bab=abbb with [2] bab=abbb:

ba b bab

Critical pair: baabbb=abbbab.

Reduce LHS:

[1]	b(aa)bbb
[2]	⇒ (bab)bb
	⇒ abbbbb

Reduce RHS:

[2]	abb(bab)
[2]	⇒ ab(bab)bb
[2]	⇒ a(bab)bbbb
[1]	⇒ (aa)bbbbbbb
	⇒ abbbbbbb

Flip LHS and RHS.

Defines rule #1.