#2432 ⟨a, b | aaabaa=babb⟩

Properties

Sum of relation sides is 10
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaabaab^-1ab^-1b^-1⟩
- Embedding: φ(a) = a, φ(b) = ba^-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.	bab² ⇒ a³ba²	[1]
2.	(a³b)²b ⇒ b(aba²)²	[2]

# ab:aaabaa=babb a/b - -
babb=aaabaa
aaabaaabb=babaaabaa

1 unique, 1 total

Σ	#	Presentation	Properties
10	1644	⟨a, b \| aaabbabaa=b⟩	Can Inf