#2220 ⟨a, b | aabaaba=bab⟩

Properties

Sum of relation sides is 10
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaababbb⟩
- Embedding: φ(a) = ba, φ(b) = a^-1b^-1a^-1

Format:	Pretty Plain
Word:
	Enter a word above to compute its normal form. Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Strategy:	Leftmost Rightmost
Result:	1 1

#	Rule	Proof
1.	a²b²ab ⇒ (ba)³	[2]
2.	(a²b)²a ⇒ bab	[1]

# ab:aabaaba=bab ba - -
aabbab=bababa
aabaaba=bab

3 unique, 5 total

Σ	#	Presentation	Properties	φ
8	310	⟨a, b \| aababbba=1⟩	Grp Inf	2
8	450	⟨a, b \| aababa=bb⟩	Can Inf
10	1792	⟨a, b \| ababbabba=b⟩	Can Inf