#2334 ⟨a, b | abababa=bbb⟩

Properties

Sum of relation sides is 10
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaaabbbb⟩
- Embedding: φ(a) = ba, 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.	b⁴a ⇒ ab⁴	[2]
2.	a(ba)³ ⇒ b³	[1]

# ab:abababa=bbb ab - -
bbbba=abbbb
abababa=bbb

2 unique, 3 total

Σ	#	Presentation	Properties	φ
8	298	⟨a, b \| aaabbbba=1⟩	Grp Inf	1
8	594	⟨a, b \| bbbb=aaaa⟩	Can Inf