Certificate for #12240 ⟨a, b | aaab=aa, bbbb=a⟩

Completion settings:

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

[1] aaab=aa

Axiom: aaab=aa.

Referenced by [3].

[2] a=bbbb

Axiom: bbbb=a.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[3] aaab=bbbbbbbb

Simplify [1] aaab=aa.

Reduce RHS:

[2]	(a)a
[2]	⇒ bbbb(a)
	⇒ bbbbbbbb

Referenced by [4].

[4] bbbbbbbbbbbbb=bbbbbbbb

Overlap of [3] aaab=bbbbbbbb with [2] a=bbbb:

aaab a

Critical pair: bbbbaab=bbbbbbbb.

Reduce LHS:

[2]	bbbb(a)ab
[2]	⇒ bbbbbbbb(a)b
	⇒ bbbbbbbbbbbbb

Defines rule #1.