#5436 ⟨a, b | aaaaaa=bbbbb⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a⁴ba has infinite order
Submonoid of enveloping group: ⟨a, b | aaaaaabbbbb⟩
- 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.	a⁶ ⇒ b⁵	[1]
2.	b⁵a ⇒ ab⁵	[2]

# ab:aaaaaa=bbbbb ab - -
aaaaaa=bbbbb
bbbbba=abbbbb

1 unique, 5 total

Σ	#	Presentation	Properties	φ
11	2839	⟨a, b \| aaaaabbbbba=1⟩	Grp Inf	4