#3371 ⟨a, b | aaaabaaaba=b⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaaabab^-1b^-1⟩
- Anti-isomorphic embedding: φ(a) = a, φ(b) = b^-1a^-1a^-1a^-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.	a⁴ba³b² ⇒ b(a³b)²a	[2]
2.	a(a³b)²a ⇒ b	[1]

# ab:aaaabaaaba=b ba - -
aaaabaaabb=baaabaaaba
aaaabaaaba=b

6 unique, 11 total

Σ	#	Presentation	Properties	φ
8	423	⟨a, b \| aaaaba=bb⟩	Can Inf
9	1022	⟨a, b \| aaaaba=bab⟩	Can Inf
10	2398	⟨a, b \| aaaaba=baab⟩	Can Inf
11	3068	⟨a, b \| aababababba=1⟩	Grp Inf	5
11	3771	⟨a, b \| ababababba=b⟩	Can Inf
11	5486	⟨a, b \| aaaaba=baaab⟩	Can Inf

3 unique, 3 total

Σ	#	Presentation	Properties
8	354	⟨a, b \| aaaabba=b⟩	Can Inf
9	752	⟨a, b \| aaaababa=b⟩	Can Inf
10	1584	⟨a, b \| aaaabaaba=b⟩	Can Inf