Certificate for #15439 ⟨a, b | aaa=aa, bbbbb=a⟩

Completion settings:

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

[1] aaa=aa

Axiom: aaa=aa.

Referenced by [3].

[2] a=bbbbb

Axiom: bbbbb=a.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[3] aaa=bbbbbbbbbb

Simplify [1] aaa=aa.

Reduce RHS:

[2]	(a)a
[2]	⇒ bbbbb(a)
	⇒ bbbbbbbbbb

Referenced by [4].

[4] bbbbbbbbbbbbbbb=bbbbbbbbbb

Overlap of [3] aaa=bbbbbbbbbb with [2] a=bbbbb:

aaa a

Critical pair: bbbbbaa=bbbbbbbbbb.

Reduce LHS:

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

Defines rule #1.