#3679 ⟨a, b | aa=1, bbbb=bbb⟩

Properties

Sum of relation sides is 9
Isomorphic to ℤ₂ ∗ ℕ_{(4 = 3)}
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b³ = b³ and b ⋅ b² = b³, however b³ ≠ b²
Not right cancellative, because right multiplication by b is not injective:
- b³ ⋅ b = b³ and b² ⋅ b = b³, however b³ ≠ b²

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.	b⁴ ⇒ b³	[2]

# ab:aa=1,bbbb=bbb ab - -
aa=1
bbbb=bbb

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

6 total

Σ	#	Presentation	Mapping
11	27611	⟨a, b \| aa=1, aabbbb=bbb⟩	φ(a) = a, φ(b) = b
11	27725	⟨a, b \| aa=1, baabbb=bbb⟩	φ(a) = a, φ(b) = b
11	27753	⟨a, b \| aa=1, bbaabb=bbb⟩	φ(a) = a, φ(b) = b
11	28139	⟨a, b \| aa=1, aabbb=bbbb⟩	φ(a) = a, φ(b) = b
11	28215	⟨a, b \| aa=1, abbbb=abbb⟩	φ(a) = a, φ(b) = b
11	28249	⟨a, b \| aa=1, baabb=bbbb⟩	φ(a) = a, φ(b) = b