#5305 ⟨a, b | abaaaba=babb⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aababa^-1bba^-1b⟩
- Anti-isomorphic embedding: φ(a) = b, φ(b) = a^-1b^-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.	bab² ⇒ aba³ba	[1]
2.	(aba²)²b² ⇒ (ba)³a²ba	[2]

# ab:abaaaba=babb a/b - -
babb=abaaaba
abaaabaabb=bababaaaba

2 unique, 9 total

Σ	#	Presentation	Properties	φ
11	3046	⟨a, b \| aabaabbabba=1⟩	Grp Inf	7
11	3651	⟨a, b \| aabbababba=b⟩	Can Inf