Certificate for #21110 ⟨a, b | bb=aa, abab=aaa⟩

Completion settings:

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

[1] bb=aa

Axiom: bb=aa.

Defines rule #4.

Referenced by [3], [4], [6], [7].

[2] abab=aaa

Axiom: abab=aaa.

Defines rule #5.

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

[3] aab=baa

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

b b bb

Critical pair: baa=aab.

Flip LHS and RHS.

Defines rule #3.

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

[4] abaaa=abaa

Overlap of [2] abab=aaa with [1] bb=aa:

aba b bb

Critical pair: abaaa=aaab.

Reduce RHS:

[3]	a(aab)
	⇒ abaa

Referenced by [5].

[5] abaa=baaaa

Overlap of [2] abab=aaa with [2] abab=aaa:

ab ab abab

Critical pair: abaaa=aaaab.

Reduce LHS:

[4]	(abaaa)
	⇒ abaa

Reduce RHS:

[3]	aa(aab)
[3]	⇒ (aab)aa
	⇒ baaaa

Defines rule #2.

Referenced by [6], [7].

[6] aaaaaa=aaaa

Overlap of [3] aab=baa with [2] abab=aaa:

a ab abab

Critical pair: aaaa=baaab.

Reduce RHS:

[3]	ba(aab)
[5]	⇒ b(abaa)
[1]	⇒ (bb)aaaa
	⇒ aaaaaa

Flip LHS and RHS.

Referenced by [7].

[7] aaaaa=aaaa

Overlap of [5] abaa=baaaa with [3] aab=baa:

ab aa aab

Critical pair: abbaa=baaaab.

Reduce LHS:

[1]	a(bb)aa
	⇒ aaaaa

Reduce RHS:

[3]	baa(aab)
[3]	⇒ b(aab)aa
[1]	⇒ (bb)aaaa
[6]	⇒ (aaaaaa)
	⇒ aaaa

Defines rule #1.