#4305 ⟨a, b | abababbba=bb⟩

Properties

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

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.	(ab)³b²a ⇒ b²	[1]
2.	(ab)³b⁴ ⇒ b³abab³a	[2]

# ab:abababbba=bb ba - -
abababbba=bb
abababbbbb=bbbababbba

1 unique, 1 total

Σ	#	Presentation	Properties
9	1056	⟨a, b \| aaabba=bbb⟩	Can Inf

2 unique, 2 total

Σ	#	Presentation	Properties
9	924	⟨a, b \| aaabbba=bb⟩	Can Inf
11	3777	⟨a, b \| abababbbba=b⟩	Can Inf