#5581 ⟨a, b | aaabab=baaaa⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaaabba^-1a^-1a^-1b^-1⟩
- Anti-isomorphic embedding: φ(a) = a^-1, φ(b) = ab

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.	a³bab ⇒ ba⁴	[1]

# ab:aaabab=baaaa ab - -
aaabab=baaaa

3 unique, 3 total

Σ	#	Presentation	Properties
10	2413	⟨a, b \| aaaabb=baaa⟩	Can Inf
10	2734	⟨a, b \| baaaa=aaabb⟩	Can Inf
11	4971	⟨a, b \| aaaabab=baaa⟩	Can Inf