#2070 ⟨a, b | ababbbba=bb⟩

Properties

Sum of relation sides is 10
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaabba^-1a^-1a^-1b⟩
- 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.	abab⁴a ⇒ b²	[1]
2.	abab⁶ ⇒ b³ab⁴a	[2]

# ab:ababbbba=bb ba - -
ababbbba=bb
ababbbbbb=bbbabbbba

2 unique, 2 total

Σ	#	Presentation	Properties
9	1102	⟨a, b \| aabbba=bbb⟩	Can Inf
11	3822	⟨a, b \| abbabbbbba=b⟩	Can Inf