#229 ⟨a, b | ababa=bb⟩

Properties

Sum of relation sides is 7
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaabbb⟩
- 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.	b³a ⇒ ab³	[2]
2.	a(ba)² ⇒ b²	[1]

# ab:ababa=bb ab - -
bbba=abbb
ababa=bb

5 unique, 14 total

Σ	#	Presentation	Properties	φ
6	67	⟨a, b \| aabbba=1⟩	Grp Inf	8
6	124	⟨a, b \| bbb=aaa⟩	Can Inf
8	410	⟨a, b \| abbabba=b⟩	Can Inf	1
9	1115	⟨a, b \| abaaba=bab⟩	Can Inf
11	5304	⟨a, b \| abaaaba=baab⟩	Can Inf