Certificate for #14367 ⟨a, b | aaaa=a, bbbbb=a⟩

Completion settings:

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

[1] aaaa=a

Axiom: aaaa=a.

Referenced by [3].

[2] a=bbbbb

Axiom: bbbbb=a.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[3] aaaa=bbbbb

Simplify [1] aaaa=a.

Reduce RHS:

[2]	(a)
	⇒ bbbbb

Referenced by [4].

[4] bbbbbbbbbbbbbbbbbbbb=bbbbb

Overlap of [3] aaaa=bbbbb with [2] a=bbbbb:

aaaa a

Critical pair: bbbbbaaa=bbbbb.

Reduce LHS:

[2]	bbbbb(a)aa
[2]	⇒ bbbbbbbbbb(a)a
[2]	⇒ bbbbbbbbbbbbbbb(a)
	⇒ bbbbbbbbbbbbbbbbbbbb

Defines rule #1.