#543 ⟨a, b | abaab=bba⟩

Properties

Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aabab^-1a^-1bb⟩
- Embedding: φ(a) = ba, φ(b) = b^-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.	b²a ⇒ aba²b	[1]

# ab:abaab=bba reversed:a/b - -
bba=abaab

5 unique, 5 total

Σ	#	Presentation	Properties
8	459	⟨a, b \| aabbab=ba⟩	Can Inf
10	1960	⟨a, b \| aababaab=ba⟩	Can Inf
10	2028	⟨a, b \| abaaabab=ba⟩	Can Inf
10	2325	⟨a, b \| ababaab=baa⟩	Can Inf
10	2573	⟨a, b \| abaaab=baba⟩	Can Inf