#2468 ⟨a, b | aaabba=bbbb⟩

Properties

Sum of relation sides is 10
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaaabbba^-1a^-1b⟩
- Embedding: φ(a) = b, φ(b) = a^-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.	a³b²ab ⇒ ba³b²a	[2]
2.	b⁴ ⇒ a³b²a	[1]

# ab:aaabba=bbbb a/b - -
aaabbab=baaabba
bbbb=aaabba

1 unique, 1 total

Σ	#	Presentation	Properties
10	1934	⟨a, b \| aaabbbba=bb⟩	Can Inf