Certificate for #16301 ⟨a, b | aab=bb, abbb=aa⟩

Completion settings:

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

[1] bb=aab

Axiom: aab=bb.

Flip LHS and RHS.

Referenced by [2], [3], [4], [8].

[2] aaaaab=aa

Axiom: abbb=aa.

Reduce LHS:

[1]	a(bb)b
[1]	⇒ aaa(bb)
	⇒ aaaaab

Referenced by [4], [6], [7].

[3] baab=aaaab

Overlap of [1] bb=aab with [1] bb=aab:

b b bb

Critical pair: baab=aabb.

Reduce RHS:

[1]	aa(bb)
	⇒ aaaab

Referenced by [5].

[4] aab=aaaa

Overlap of [2] aaaaab=aa with [1] bb=aab:

aaaaa b bb

Critical pair: aaaaaaab=aab.

Reduce LHS:

[2]	aa(aaaaab)
	⇒ aaaa

Flip LHS and RHS.

Defines rule #3.

Referenced by [5], [7], [8].

[5] baaaa=aaaaaa

Simplify [3] baab=aaaab.

Reduce LHS:

[4]	b(aab)
	⇒ baaaa

Reduce RHS:

[4]	aa(aab)
	⇒ aaaaaa

Referenced by [6].

[6] baa=aaaa

Overlap of [5] baaaa=aaaaaa with [2] aaaaab=aa:

b aaaa aaaaab

Critical pair: baa=aaaaaaab.

Reduce RHS:

[2]	aa(aaaaab)
	⇒ aaaa

Defines rule #2.

Referenced by [7].

[7] aaaaaaa=aa

Overlap of [6] baa=aaaa with [4] aab=aaaa:

ba a aab

Critical pair: baaaaa=aaaaab.

Reduce LHS:

[6]	(baa)aaa
	⇒ aaaaaaa

Reduce RHS:

[2]	(aaaaab)
	⇒ aa

Defines rule #1.

[8] bb=aaaa

Simplify [1] bb=aab.

Reduce RHS:

[4]	(aab)
	⇒ aaaa

Defines rule #4.