#966 ⟨a, b | aabbbba=bb⟩

Properties

Sum of relation sides is 9
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaaabba^-1a^-1b⟩
- Anti-isomorphic embedding: φ(a) = b, φ(b) = a

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.	a²b⁴a ⇒ b²	[1]
2.	a²b⁶ ⇒ b²ab⁴a	[2]

# ab:aabbbba=bb ba - -
aabbbba=bb
aabbbbbb=bbabbbba

4 unique, 11 total

Σ	#	Presentation	Properties	φ
9	1238	⟨a, b \| aabba=bbbb⟩	Can Inf
10	2342	⟨a, b \| ababbba=bbb⟩	Can Inf
11	2815	⟨a, b \| aaaaabaabba=1⟩	Grp Inf	7
11	4350	⟨a, b \| abbabbbba=bb⟩	Can Inf

1 unique, 1 total

Σ	#	Presentation	Properties
10	1798	⟨a, b \| ababbbbba=b⟩	Can Inf