#17665 ⟨a, b | aaaa=1, abbbb=ab⟩

Properties

Sum of relation sides is 11
Isomorphic to ℤ₄ ∗ ℕ_{(4 = 1)}
Infinite non-cancellative non-commutative monoid
Element a²ba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b³ = b and b ⋅ 1 = b, however b³ ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- b³ ⋅ b = b and 1 ⋅ b = b, however b³ ≠ 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.	a⁴ ⇒ 1	[1]
2.	b⁴ ⇒ b	[3]

# ab:aaaa=1,abbbb=ab ab - -
aaaa=1
bbbb=b