#4366 ⟨a, b | aaaaaaaa=bbb⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a⁶ba has infinite order
Submonoid of enveloping group: ⟨a, b | aaaaaaaabbb⟩
- Embedding: φ(a) = a, 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.	b³a ⇒ ab³	[2]
2.	a⁸ ⇒ b³	[1]

# ab:aaaaaaaa=bbb ab - -
bbba=abbb
aaaaaaaa=bbb

1 unique, 5 total

Σ	#	Presentation	Properties	φ
11	2791	⟨a, b \| aaaaaaabbba=1⟩	Grp Inf	4