#4091 ⟨a, b | aabaababa=bb⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aababab^-1b^-1ab^-1⟩
- Anti-isomorphic 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.	(a²b)²aba ⇒ b²	[1]
2.	b²(aba)²ba ⇒ (a²b)²ab³	[2]

# ab:aabaababa=bb ab - -
aabaababa=bb
bbabaababa=aabaababbb

3 unique, 9 total

Σ	#	Presentation	Properties	φ
11	3040	⟨a, b \| aabaababbba=1⟩	Grp Inf	6
11	3612	⟨a, b \| aababbabba=b⟩	Can Inf
11	5146	⟨a, b \| aabaaba=bbab⟩	Can Inf