#534 ⟨a, b | aabba=bab⟩

Properties

Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aabab^-1abb⟩
- Embedding: φ(a) = aba, φ(b) = b^-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.	a²b²a ⇒ bab	[1]
2.	a²b³ab ⇒ (ba)²b²a	[2]

# ab:aabba=bab ba - -
aabba=bab
aabbbab=bababba

5 unique, 10 total

Σ	#	Presentation	Properties	φ
8	400	⟨a, b \| abaabba=b⟩	Can Inf
10	1419	⟨a, b \| aababaabba=1⟩	Grp Inf	5
10	1758	⟨a, b \| abaaababa=b⟩	Can Inf
10	2340	⟨a, b \| ababbba=bab⟩	Can Inf
10	2504	⟨a, b \| aababa=baab⟩	Can Inf