#400 ⟨a, b | abaabba=b⟩

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) = ab, φ(b) = b^-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.	aba²b³ ⇒ b²a²b²a	[2]
2.	aba²b²a ⇒ b	[1]

# ab:abaabba=b ba - -
abaabbb=bbaabba
abaabba=b

5 unique, 10 total

Σ	#	Presentation	Properties	φ
8	534	⟨a, b \| aabba=bab⟩	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