#490 ⟨a, b | aaaaa=bbb⟩

Properties

Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element a³ba has infinite order
Submonoid of enveloping group: ⟨a, b | aaaaabbb⟩
- 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.	a⁵ ⇒ b³	[1]

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

5 unique, 12 total

Σ	#	Presentation	Properties	φ
8	283	⟨a, b \| aaaabbba=1⟩	Grp Inf	7
9	1264	⟨a, b \| ababa=bbbb⟩	Can Inf
10	2356	⟨a, b \| abbabba=bbb⟩	Can Inf
11	4301	⟨a, b \| ababababa=bb⟩	Can Inf
11	4357	⟨a, b \| abbbabbba=bb⟩	Can Inf