#4496 ⟨a, b | aaabaaba=bab⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaababab^-1b^-1⟩
- Embedding: φ(a) = a, φ(b) = a^-1b

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(a²b)²a ⇒ bab	[1]
2.	a³ba²b²ab ⇒ b(aba)³	[2]

# ab:aaabaaba=bab ba - -
aaabaaba=bab
aaabaabbab=babaabaaba

2 unique, 4 total

Σ	#	Presentation	Properties	φ
9	908	⟨a, b \| aaababa=bb⟩	Can Inf
10	1425	⟨a, b \| aabababbba=1⟩	Grp Inf	2