#830 ⟨a, b | aabbbbba=b⟩

Properties

Sum of relation sides is 9
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaaaabba^-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.	a²b⁶ ⇒ bab⁵a	[2]
2.	a²b⁵a ⇒ b	[1]

# ab:aabbbbba=b ba - -
aabbbbbb=babbbbba
aabbbbba=b

4 unique, 10 total

Σ	#	Presentation	Properties	φ
9	1147	⟨a, b \| aaaaa=babb⟩	Can Inf
10	1297	⟨a, b \| aaaaababba=1⟩	Grp Inf	6
10	2614	⟨a, b \| ababba=bbbb⟩	Can Inf
11	4878	⟨a, b \| abbabbba=bbb⟩	Can Inf