#2372 ⟨a, b | aaaaaa=bbbb⟩

Properties

Sum of relation sides is 10
Infinite cancellative non-commutative monoid
Element a⁴ba has infinite order
Submonoid of enveloping group: ⟨a, b | aaaaaabbbb⟩
- 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.	b⁴a ⇒ ab⁴	[2]
2.	a⁶ ⇒ b⁴	[1]

# ab:aaaaaa=bbbb ab - -
bbbba=abbbb
aaaaaa=bbbb

1 unique, 5 total

Σ	#	Presentation	Properties	φ
10	1305	⟨a, b \| aaaaabbbba=1⟩	Grp Inf	4