#1146 ⟨a, b | aaaaa=baab⟩

Properties

Sum of relation sides is 9
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaaaaaabb⟩
- 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.	a⁷b ⇒ ba⁷	[2]
2.	ba²b ⇒ a⁵	[1]

# ab:aaaaa=baab a/b - -
aaaaaaab=baaaaaaa
baab=aaaaa

7 unique, 15 total

Σ	#	Presentation	Properties	φ
9	601	⟨a, b \| aaaaaabba=1⟩	Grp Inf	8
9	866	⟨a, b \| abbbbbba=b⟩	Can Inf
9	869	⟨a, b \| aaaaaaa=bb⟩	Can Inf
9	1002	⟨a, b \| abbbbba=bb⟩	Can Inf
9	1007	⟨a, b \| aaaaaa=bab⟩	Can Inf
9	1138	⟨a, b \| abbbba=bbb⟩	Can Inf
9	1274	⟨a, b \| abbba=bbbb⟩	Can Inf