#5274 ⟨a, b | aba=bb, aaaa=a⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 10
Infinite non-commutative monoid

Rewriting system

Format:	Pretty Plain
Word to reduce:
	Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Reduction strategy:	Leftmost Rightmost
Path to normal form:	1 1

Reduction order:
- Left-to-right recursive path with deg(b) = 0; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	b¹⁰ ⇒ b⁴	[11]
2.	bab⁹ ⇒ bab³	[12]
3.	b³a ⇒ ab³	[3]
4.	a²b⁴ ⇒ bab⁸	[10]
5.	aba ⇒ b²	[1]
6.	ab²ab³ ⇒ b²ab⁵	[8]
7.	ba²b³ ⇒ b²ab⁷	[9]
8.	b²a²b² ⇒ ab³	[6]
9.	a³b² ⇒ b²	[5]
10.	b²a³ ⇒ b²	[4]
11.	a⁴ ⇒ a	[2]

# ab:aba=bb,aaaa=a b/a
bbbbbbbbbb=bbbb
babbbbbbbbb=babbb
bbba=abbb
aabbbb=babbbbbbbb
aba=bb
abbabbb=bbabbbbb
baabbb=bbabbbbbbb
bbaabb=abbb
aaabb=bb
bbaaa=bb
aaaa=a

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