Certificate for #5303 ⟨a, b | aaa=aa, abb=ba⟩

Completion settings:

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

[1] aaa=aa

Axiom: aaa=aa.

Defines rule #3.

Referenced by [3].

[2] ba=abb

Axiom: abb=ba.

Flip LHS and RHS.

Defines rule #1.

Referenced by [3].

[3] aabbbbbbbb=aabbbb

Overlap of [2] ba=abb with [1] aaa=aa:

b a aaa

Critical pair: baa=abbaa.

Reduce LHS:

[2]	(ba)a
[2]	⇒ ab(ba)
[2]	⇒ a(ba)bb
	⇒ aabbbb

Reduce RHS:

[2]	ab(ba)a
[2]	⇒ a(ba)bba
[2]	⇒ aabbb(ba)
[2]	⇒ aabb(ba)bb
[2]	⇒ aab(ba)bbbb
[2]	⇒ aa(ba)bbbbbb
[1]	⇒ (aaa)bbbbbbbb
	⇒ aabbbbbbbb

Flip LHS and RHS.

Defines rule #2.