#4138 ⟨a, b | aababbaba=bb⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaababba^-1bb⟩
- Embedding: φ(a) = ab, 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.	a²(bab)²a ⇒ b²	[1]
2.	a²bab²ab³ ⇒ (b(ba)²)²	[2]

# ab:aababbaba=bb ba - -
aababbaba=bb
aababbabbb=bbababbaba

2 unique, 2 total

Σ	#	Presentation	Properties
10	1704	⟨a, b \| aababbbaa=b⟩	Can Inf
11	5704	⟨a, b \| aababa=bbabb⟩	Can Inf