#1999 ⟨a, b | aabbabba=bb⟩

Properties

Sum of relation sides is 10
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaaabaabbb⟩
- Embedding: φ(a) = aab, 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.	a²(b²a)² ⇒ b²	[1]
2.	a²b²ab⁴ ⇒ (b²a)³	[2]

# ab:aabbabba=bb ba - -
aabbabba=bb
aabbabbbb=bbabbabba

1 unique, 7 total

Σ	#	Presentation	Properties	φ
10	1350	⟨a, b \| aaabaabbba=1⟩	Grp Inf	6