#1180 ⟨a, b | aaaba=bbbb⟩

Properties

Sum of relation sides is 9
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaaabbba^-1b⟩
- Embedding: φ(a) = b, 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.	a³bab ⇒ ba³ba	[2]
2.	b⁴ ⇒ a³ba	[1]

# ab:aaaba=bbbb a/b - -
aaabab=baaaba
bbbb=aaaba

2 unique, 8 total

Σ	#	Presentation	Properties	φ
11	2861	⟨a, b \| aaaabababba=1⟩	Grp Inf	6
11	4830	⟨a, b \| abababba=bbb⟩	Can Inf

1 unique, 1 total

Σ	#	Presentation	Properties
9	788	⟨a, b \| aaabbbba=b⟩	Can Inf