Certificate for #25217 ⟨a, b | aa=a, abbbb=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=abbbb

Axiom: abbbb=bab.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3].

[3] abbbbbbbbbbbbb=abbbbbbb

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

ba b bab

Critical pair: baabbbb=abbbbab.

Reduce LHS:

[1]	b(aa)bbbb
[2]	⇒ (bab)bbb
	⇒ abbbbbbb

Reduce RHS:

[2]	abbb(bab)
[2]	⇒ abb(bab)bbb
[2]	⇒ ab(bab)bbbbbb
[2]	⇒ a(bab)bbbbbbbbb
[1]	⇒ (aa)bbbbbbbbbbbbb
	⇒ abbbbbbbbbbbbb

Flip LHS and RHS.

Defines rule #1.