#2083 ⟨a, b | aab=b, bbbb=b⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element a 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:
- a² ⋅ b = b and 1 ⋅ b = b, however a² ≠ 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.	a²b ⇒ b	[1]
2.	b⁴ ⇒ b	[2]

# ab:aab=b,bbbb=b ab - -
aab=b
bbbb=b

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

7 total

Σ	#	Presentation	Mapping
11	12489	⟨a, b \| aabb=bb, bbbb=b⟩	φ(a) = a, φ(b) = b
11	18991	⟨a, b \| aab=b, aabbbb=b⟩	φ(a) = a, φ(b) = b
11	19039	⟨a, b \| aab=b, baabbb=b⟩	φ(a) = a, φ(b) = b
11	19063	⟨a, b \| aab=b, bbaabb=b⟩	φ(a) = a, φ(b) = b
11	19075	⟨a, b \| aab=b, bbbaab=b⟩	φ(a) = a, φ(b) = b
11	19565	⟨a, b \| aab=b, abbbb=ab⟩	φ(a) = a, φ(b) = b
11	20169	⟨a, b \| aab=b, bbbb=aab⟩	φ(a) = a, φ(b) = b