Certificate for #1584 ⟨a, b | aaa=aa, bbb=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=bbb

Axiom: bbb=a.

Flip LHS and RHS.

Defines rule #2.

Referenced by [3], [4].

[3] aaa=bbbbbb

Simplify [1] aaa=aa.

Reduce RHS:

[2]	(a)a
[2]	⇒ bbb(a)
	⇒ bbbbbb

Referenced by [4].

[4] bbbbbbbbb=bbbbbb

Overlap of [3] aaa=bbbbbb with [2] a=bbb:

aaa a

Critical pair: bbbaa=bbbbbb.

Reduce LHS:

[2]	bbb(a)a
[2]	⇒ bbbbbb(a)
	⇒ bbbbbbbbb

Defines rule #1.