#1203 ⟨a, b | aa=1, bbbb=bb⟩

Properties

Sum of relation sides is 8
Isomorphic to ℤ₂ ∗ ℕ_{(4 = 2)}
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b³ = b² and b ⋅ b = b², however b³ ≠ b
Not right cancellative, because right multiplication by b is not injective:
- b³ ⋅ b = b² and b ⋅ b = b², however b³ ≠ 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.	b⁴ ⇒ b²	[2]

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

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

6 total

Σ	#	Presentation	Mapping
10	9985	⟨a, b \| aa=1, aabbbb=bb⟩	φ(a) = a, φ(b) = b
10	10042	⟨a, b \| aa=1, baabbb=bb⟩	φ(a) = a, φ(b) = b
10	10056	⟨a, b \| aa=1, bbaabb=bb⟩	φ(a) = a, φ(b) = b
10	10299	⟨a, b \| aa=1, abbbb=abb⟩	φ(a) = a, φ(b) = b
10	10532	⟨a, b \| aa=1, bbbb=aabb⟩	φ(a) = a, φ(b) = b
10	10536	⟨a, b \| aa=1, bbbb=baab⟩	φ(a) = a, φ(b) = b