#2765 ⟨a, b | babab=aaaba⟩

Properties

Sum of relation sides is 10
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaabab^-1b^-1b^-1⟩
- Anti-isomorphic embedding: φ(a) = a^-1, φ(b) = ab^-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.	a(a²b)² ⇒ ba⁴ba	[2]
2.	b(ab)² ⇒ a³ba	[1]

# ab:babab=aaaba a/b - -
aaabaab=baaaaba
babab=aaaba

3 unique, 8 total

Σ	#	Presentation	Properties	φ
8	506	⟨a, b \| aaaba=bbb⟩	Can Inf
10	1356	⟨a, b \| aaabababba=1⟩	Grp Inf	5
10	2059	⟨a, b \| abababba=bb⟩	Can Inf

2 unique, 2 total

Σ	#	Presentation	Properties
8	370	⟨a, b \| aaabbba=b⟩	Can Inf
10	1628	⟨a, b \| aaabababa=b⟩	Can Inf