#4130 ⟨a, b | aabababba=bb⟩

Properties

Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaababbbab^-1⟩
- Anti-isomorphic embedding: φ(a) = ab, φ(b) = b^-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.	a(ab)³ba ⇒ b²	[1]
2.	a(ab)³b³ ⇒ b(ba)³b²a	[2]

# ab:aabababba=bb ba - -
aabababba=bb
aabababbbb=bbabababba

2 unique, 2 total

Σ	#	Presentation	Properties
10	1636	⟨a, b \| aaababbba=b⟩	Can Inf
11	5706	⟨a, b \| aababa=bbbab⟩	Can Inf