#2370 ⟨a, b | aaaaaa=baab⟩

Properties

Sum of relation sides is 10
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaaaaaaabb⟩
- Embedding: φ(a) = a, φ(b) = b^-1a^-1a^-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.	a⁸b ⇒ ba⁸	[2]
2.	ba²b ⇒ a⁶	[1]

# ab:aaaaaa=baab a/b - -
aaaaaaaab=baaaaaaaa
baab=aaaaaa

8 unique, 12 total

Σ	#	Presentation	Properties	φ
10	1281	⟨a, b \| aaaaaaabba=1⟩	Grp Inf	4
10	1818	⟨a, b \| abbbbbbba=b⟩	Can Inf
10	1821	⟨a, b \| aaaaaaaa=bb⟩	Can Inf
10	2090	⟨a, b \| abbbbbba=bb⟩	Can Inf
10	2095	⟨a, b \| aaaaaaa=bab⟩	Can Inf
10	2362	⟨a, b \| abbbbba=bbb⟩	Can Inf
10	2634	⟨a, b \| abbbba=bbbb⟩	Can Inf
10	2741	⟨a, b \| baaab=aaaaa⟩	Can Inf