Certificate for #7152 ⟨a, b | bb=aa, abab=aa⟩

Completion settings:

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

[1] bb=aa

Axiom: bb=aa.

Defines rule #5.

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

[2] abab=aa

Axiom: abab=aa.

Defines rule #6.

Referenced by [4], [5].

[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 #4.

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

[4] abaaa=baa

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

aba b bb

Critical pair: abaaa=aab.

Reduce RHS:

[3]	(aab)
	⇒ baa

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

[5] babaa=aaa

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

a ab abab

Critical pair: aaa=baaab.

Reduce RHS:

[3]	ba(aab)
	⇒ babaa

Flip LHS and RHS.

Referenced by [7].

[6] abaa=baaaaa

Overlap of [3] aab=baa with [4] abaaa=baa:

a ab abaaa

Critical pair: abaa=baaaaa.

Defines rule #3.

Referenced by [8].

[7] aaaaaaa=aaa

Overlap of [4] abaaa=baa with [3] aab=baa:

abaa a aab

Critical pair: abaabaa=baaab.

Reduce LHS:

[3]	ab(aab)aa
[1]	⇒ a(bb)aaaa
	⇒ aaaaaaa

Reduce RHS:

[3]	ba(aab)
[5]	⇒ (babaa)
	⇒ aaa

Defines rule #1.

[8] baaaaaa=baa

Overlap of [4] abaaa=baa with [6] abaa=baaaaa:

abaaa abaa

Critical pair: baaaaaa=baa.

Defines rule #2.