#10063 ⟨a, b | aa=1, bbbbbb=bb⟩

Properties

Sum of relation sides is 10
Isomorphic to ℤ₂ ∗ ℕ_{(6 = 2)}
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b⁵ = b² and b ⋅ b = b², however b⁵ ≠ b
Not right cancellative, because right multiplication by b is not injective:
- b⁵ ⋅ b = b² and b ⋅ b = b², however b⁵ ≠ b

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 ⇒ 1	[1]
2.	b⁶ ⇒ b²	[2]

# ab:aa=1,bbbbbb=bb ab - -
aa=1
bbbbbb=bb