#592 ⟨a, b | babb=abaa⟩

Properties

Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aababbab^-1⟩
- Embedding: φ(a) = a^-1b^-1, φ(b) = bab^-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.	bab² ⇒ aba²	[1]
2.	(ba)³a ⇒ aba³b²	[2]

# ab:babb=abaa ab - -
babb=abaa
bababaa=abaaabb

4 unique, 9 total

Σ	#	Presentation	Properties	φ
8	382	⟨a, b \| aababba=b⟩	Can Inf
10	1408	⟨a, b \| aabaababba=1⟩	Grp Inf	5
10	1678	⟨a, b \| aabaababa=b⟩	Can Inf
10	2612	⟨a, b \| ababba=bbab⟩	Can Inf