Certificate for #16067 ⟨a, b | aaa=bb, abbb=aa⟩

Completion settings:

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

[1] bb=aaa

Axiom: aaa=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [2], [3], [5], [7].

[2] aaaab=aa

Axiom: abbb=aa.

Reduce LHS:

[1]	a(bb)b
	⇒ aaaab

Referenced by [4].

[3] aaab=baaa

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

b b bb

Critical pair: baaa=aaab.

Flip LHS and RHS.

Referenced by [4], [5], [6], [7].

[4] abaaa=aa

Simplify [2] aaaab=aa.

Reduce LHS:

[3]	a(aaab)
	⇒ abaaa

Referenced by [5], [6], [7], [8], [9].

[5] aab=aaaaaaa

Overlap of [4] abaaa=aa with [3] aaab=baaa:

ab aaa aaab

Critical pair: abbaaa=aab.

Reduce LHS:

[1]	a(bb)aaa
	⇒ aaaaaaa

Flip LHS and RHS.

Defines rule #3.

Referenced by [9].

[6] abaa=baaa

Overlap of [4] abaaa=aa with [3] aaab=baaa:

aba aa aaab

Critical pair: ababaaa=aaab.

Reduce LHS:

[4]	ab(abaaa)
	⇒ abaa

Reduce RHS:

[3]	(aaab)
	⇒ baaa

Referenced by [7], [8], [9].

[7] baaaa=aaaaaaaaa

Overlap of [4] abaaa=aa with [3] aaab=baaa:

abaa a aaab

Critical pair: abaabaaa=aaaab.

Reduce LHS:

[6]	(abaa)baaa
[3]	⇒ b(aaab)aaa
[1]	⇒ (bb)aaaaaa
	⇒ aaaaaaaaa

Reduce RHS:

[3]	a(aaab)
[6]	⇒ (abaa)a
	⇒ baaaa

Flip LHS and RHS.

Referenced by [8].

[8] aaaaaaaaa=aa

Overlap of [4] abaaa=aa with [6] abaa=baaa:

abaaa abaa

Critical pair: baaaa=aa.

Reduce LHS:

[7]	(baaaa)
	⇒ aaaaaaaaa

Defines rule #1.

Referenced by [9].

[9] baa=aaaaaaa

Overlap of [4] abaaa=aa with [5] aab=aaaaaaa:

aba aa aab

Critical pair: abaaaaaaaa=aab.

Reduce LHS:

[6]	(abaa)aaaaaa
[8]	⇒ b(aaaaaaaaa)
	⇒ baa

Reduce RHS:

[5]	(aab)
	⇒ aaaaaaa

Defines rule #2.