Certificate for #12164 ⟨a, b | aaaa=aa, bbbb=a⟩

Completion settings:

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

[1] aaaa=aa

Axiom: aaaa=aa.

Referenced by [3].

[2] a=bbbb

Axiom: bbbb=a.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[3] aaaa=bbbbbbbb

Simplify [1] aaaa=aa.

Reduce RHS:

[2]	(a)a
[2]	⇒ bbbb(a)
	⇒ bbbbbbbb

Referenced by [4].

[4] bbbbbbbbbbbbbbbb=bbbbbbbb

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

aaaa a

Critical pair: bbbbaaa=bbbbbbbb.

Reduce LHS:

[2]	bbbb(a)aa
[2]	⇒ bbbbbbbb(a)a
[2]	⇒ bbbbbbbbbbbb(a)
	⇒ bbbbbbbbbbbbbbbb

Defines rule #1.