#2222 ⟨a, b | aabaaba=bbb⟩

Properties

Sum of relation sides is 10
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaabba^-1bba^-1b⟩
- Embedding: φ(a) = b, φ(b) = a^-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.	b³aba ⇒ a²b⁴	[2]
2.	(a²b)²a ⇒ b³	[1]

# ab:aabaaba=bbb ab - -
bbbaba=aabbbb
aabaaba=bbb

1 unique, 8 total

Σ	#	Presentation	Properties	φ
11	2946	⟨a, b \| aaababbabba=1⟩	Grp Inf	7