#1788 ⟨a, b | abababbba=b⟩

Properties

Sum of relation sides is 10
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaabbab^-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)³b³ ⇒ b(ba)²b³a	[2]
2.	(ab)³b²a ⇒ b	[1]

# ab:abababbba=b ba - -
abababbbb=bbababbba
abababbba=b

2 unique, 2 total

Σ	#	Presentation	Properties
8	439	⟨a, b \| aaabba=bb⟩	Can Inf
10	2172	⟨a, b \| aaababa=bab⟩	Can Inf