#489 ⟨a, b | aaaaa=bab⟩

Properties

Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaaaaabb⟩
- Embedding: φ(a) = a, φ(b) = b^-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.	a⁶b ⇒ ba⁶	[2]
2.	bab ⇒ a⁵	[1]

# ab:aaaaa=bab a/b - -
aaaaaab=baaaaaa
bab=aaaaa

6 unique, 13 total

Σ	#	Presentation	Properties	φ
8	275	⟨a, b \| aaaaabba=1⟩	Grp Inf	7
8	412	⟨a, b \| abbbbba=b⟩	Can Inf
8	415	⟨a, b \| aaaaaa=bb⟩	Can Inf
8	484	⟨a, b \| abbbba=bb⟩	Can Inf
8	556	⟨a, b \| abbba=bbb⟩	Can Inf
8	585	⟨a, b \| baab=aaaa⟩	Can Inf