#22808 ⟨a, b | aaa=1, abbab=bba⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
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.	b⁵ ⇒ b²	[9]
2.	b²ab³ ⇒ b²a	[5]
3.	b³a ⇒ ab³	[12]
4.	ab²a ⇒ b²ab²	[4]
5.	(ba)²b² ⇒ abab³	[15]
6.	b²a²b³ ⇒ b²a²	[8]
7.	b(ba)² ⇒ abab²	[13]
8.	a³ ⇒ 1	[1]
9.	a²bab² ⇒ b²a²	[14]
10.	aba²b² ⇒ ba²b⁴	[18]
11.	b²a²ba ⇒ ba²b⁴	[16]

# ab:aaa=1,abbab=bba b/a
bbbbb=bb
bbabbb=bba
bbba=abbb
abba=bbabb
bababb=ababbb
bbaabbb=bbaa
bbaba=ababb
aaa=1
aababb=bbaa
abaabb=baabbbb
bbaaba=baabbbb

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