#2243 ⟨a, b | aababab=bba⟩

Properties

Sum of relation sides is 10
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaababba^-1b^-1⟩
- Anti-isomorphic embedding: φ(a) = ab, φ(b) = ab^-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.	a(ab)³ ⇒ b²a	[1]

# ab:aababab=bba ab - -
aababab=bba

3 unique, 3 total

Σ	#	Presentation	Properties
9	911	⟨a, b \| aaababb=ba⟩	Can Inf
9	1221	⟨a, b \| aabab=bbba⟩	Can Inf
11	3973	⟨a, b \| aaabaabab=ba⟩	Can Inf

1 unique, 1 total

Σ	#	Presentation	Properties
11	5315	⟨a, b \| abaabab=baaa⟩	Can Inf