#1746 ⟨a, b | aabbbbbba=b⟩

Properties

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

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.	a²b⁷ ⇒ bab⁶a	[2]
2.	a²b⁶a ⇒ b	[1]

# ab:aabbbbbba=b ba - -
aabbbbbbb=babbbbbba
aabbbbbba=b

3 unique, 10 total

Σ	#	Presentation	Properties	φ
10	2371	⟨a, b \| aaaaaa=babb⟩	Can Inf
11	2799	⟨a, b \| aaaaaababba=1⟩	Grp Inf	7
11	5908	⟨a, b \| ababba=bbbbb⟩	Can Inf